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1.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
2.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献
3.
Itaru Terada 《Journal of Algebraic Combinatorics》2001,14(3):229-267
We interpret geometrically a variant of the Robinson-Schensted correspondence which links Brauer diagrams with updown tableaux, in the spirit of Steinberg's result [32] on the original Robinson-Schensted correspondence. Our result uses the variety of all
where
is a complete flag in
is a nondegenerate alternating bilinear form on
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both and
instead of Steinberg's variety of
where
are two complete flags in
and N is a nilpotent element of the Lie algebra of the simultaneous stabilizer of both
. 相似文献
4.
Hélène Barcelo 《Journal of Algebraic Combinatorics》1993,2(1):5-23
We describe a straightening algorithm for the action of S
n on a certain graded ring
. The ring
appears in the work of C. de Concini and C. Procesi [2] and T. Tanisaki [8], and more recently in the work of A. Garsia and C. Procesi [4]. This ring is a graded version of the permutation representation resulting from the action of S
n on the left cosets of a Young subgroup. As a corollary of our straightening algorithm we obtain a combinatorial proof of the fact that the top degree component of
affords the irreducible representation of S
n indexed by . 相似文献
5.
Patrick Headley 《Journal of Algebraic Combinatorics》1997,6(4):331-338
Let be an irreducible crystallographic rootsystem in a Euclidean space V, with + theset of positive roots. For ,
, let
be the hyperplane
. We define a set of hyperplanes
. This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of
is
, where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to . 相似文献
6.
Hiroshi Suzuki 《Journal of Algebraic Combinatorics》1998,7(2):165-180
It is well known that imprimitive P-polynomial association schemes
with
are either bipartite or antipodal, i.e., intersection numbers satisfy either
for all
for all
. In this paper, we show that imprimitive
-polynomial association schemes
with
are either dual bipartite or dual antipodal, i.e., dual intersection numbers satisfy either
. 相似文献
7.
Fabrizio Caselli 《Journal of Algebraic Combinatorics》2003,18(3):171-187
We find an explicit formula for the Kazhdan-Lusztig polynomials P
ui,a,v
i of the symmetric group
(n) where, for a, i, n
such that 1 a i n, we denote by u
i,a = s
a
s
a+1 ··· s
i–1 and by v
i the element of
(n) obtained by inserting n in position i in any permutation of
(n – 1) allowed to rise only in the first and in the last place. Our result implies, in particular, the validity of two conjectures of Brenti and Simion [4, Conjectures 4.2 and 4.3], and includes as a special case a result of Shapiro, Shapiro and Vainshtein [13, Theorem 1]. All the proofs are purely combinatorial and make no use of the geometry of the corresponding Schubert varieties. 相似文献
8.
Axel Hultman 《Journal of Algebraic Combinatorics》2002,16(1):83-96
Let
n,k,k
and
n,k,h
, h < k, denote the intersection lattices of the k-equal subspace arrangement of type
n
and the k,h-equal subspace arrangement of type
n
respectively. Denote by
the group of signed permutations. We show that (
n,k,k
)/
is collapsible. For (
n,k,h
)/
, h < k, we show the following. If n 0 (mod k), then it is homotopy equivalent to a sphere of dimension
. If n h (mod k), then it is homotopy equivalent to a sphere of dimension
. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of
on the homology groups of (
n,k,k
) and (
n,k,h
) are stated.The collapsibility of (
n,k,k
)/
is established using a discrete Morse function. The same method is used to show that (
n,k,h
)/
, h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Björner and M. Wachs (Trans. Amer. Math. Soc.
4 (1996), 1299–1327) when the cell complex is an order complex of a poset. 相似文献
9.
O. V. Sarafanov 《Journal of Mathematical Sciences》2004,120(2):1195-1239
The C
*-algebra
generated by the operators of pseudodifferential boundary value problems on a manifold
with smooth closed disjoint edges and boundary
is studied. The operators act in the space L
2(
)
L
2(
). The goal of this paper is to describe all (up to an equivalence) irreducible representations of the algebra
Bibliography: 12 titles. 相似文献
10.
Sheila Sundaram 《Journal of Algebraic Combinatorics》1995,4(1):69-92
Let
denote the subposet obtained by selecting even ranks in the partition lattice
. We show that the homology of
has dimension
, where
is the tangent number. It is thus an integral multiple of both the Genocchi number and an André or simsun number. Using the general theory of rank-selected homology representations developed in [22], we show that, for the special case of
, the character of the symmetric group S
2n
on the homology is supported on the set of involutions. Our proof techniques lead to the discovery of a family of integers b
i(n), 2 i n, defined recursively. We conjecture that, for the full automorphism group S
2n, the homology is a sum of permutation modules induced from Young subgroups of the form
, with nonnegative integer multiplicity b
i(n). The nonnegativity of the integers b
i(n) would imply the existence of new refinements, into sums of powers of 2, of the tangent number and the André or simsun number a
n(2n).Similarly, the restriction of this homology module to S
2n–1 yields a family of integers d
i(n), 1 i n – 1, such that the numbers 2–i
d
i(n) refine the Genocchi number G
2n
. We conjecture that 2–i
d
i(n) is a positive integer for all i.Finally, we present a recursive algorithm to generate a family of polynomials which encode the homology representations of the subposets obtained by selecting the top k ranks of
, 1 k n – 1. We conjecture that these are all permutation modules for S
2n
. 相似文献
11.
Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit
n_1×s×
n_k des topologies fines des espaces R
n
1,. . ., R
n
k,
n_1×s×
n_k-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique,
n_1×s×
n_k-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions
Abstract.We prove that every separately finely surperharmonic function on an open set in R
n
1×s×R
n
k for the product
n_1×s×
n_k of the fine topologies on the spaces R
n
1,. . ., R
n
k,
n_1×s×
n-klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function
n_1×s×
n
k-locally bounded in is finely harmonic. 相似文献
12.
Masato Tomiyama 《Journal of Algebraic Combinatorics》1998,7(2):197-220
Let be a distance-regular graph with diameter
and height
, where
. Suppose that for every in and every in
, the induced subgraph on
is isomorphic to a complete multipartite graph
with
. Then
and is isomorphic to the Johnson graph
. 相似文献
13.
Sara C. Billey William Jockusch Richard P. Stanley 《Journal of Algebraic Combinatorics》1993,2(4):345-374
Schubert polynomials were introduced by Bernstein et al. and Demazure, and were extensively developed by Lascoux, Schützenberger, Macdonald, and others. We give an explicit combinatorial interpretation of the Schubert polynomial
in terms of the reduced decompositions of the permutation w. Using this result, a variation of Schensted's correspondence due to Edelman and Greene allows one to associate in a natural way a certain set
of tableaux with w, each tableau contributing a single term to
. This correspondence leads to many problems and conjectures, whose interrelation is investigated. In Section 2 we consider permutations with no decreasing subsequence of length three (or 321-avoiding permutations). We show for such permutations that
is a flag skew Schur function. In Section 3 we use this result to obtain some interesting properties of the rational function
, where
denotes a skew Schur function.Sara C. Billey: Supported by the National Physical Science Consortium. William Jockusch: Supported by an NSF Graduate Fellowship. Richard P. Stanley: Partially supported by NSF grants DMS-8901834 and DMS-9206374 相似文献
14.
A spin model is a square matrix that encodes the basic data for a statistical mechanical construction of link invariants due to V.F.R. Jones. Every spin model W is contained in a canonical Bose-Mesner algebra
(W). In this paper we study the distance-regular graphs whose Bose-Mesner algebra
satisfies W
(W). Suppose W has at least three distinct entries. We show that is 1-homogeneous and that the first and the last subconstituents of are strongly regular and distance-regular, respectively. 相似文献
15.
S. S. Podkorytov 《Journal of Mathematical Sciences》2003,113(6):868-878
Let
. Assume that V is a manifold,
is the set of germs of n-dimensional oriented submanifolds of V, and
is the 2-module of all 2-valued functions on E
n
(V). If
is an oriented submanifold, let
be the indicator function of the set of germs of X. It is proved that there exists a quadratic map
such that for any compact oriented submanifold
one has the relation
, where
is the (rational) semicharacteristic of
, i.e., the residue class defined by the formula
Bibliography: 7 titles. 相似文献
16.
For a class of Serre fibratations
with a weak formal base X (or with a degenerated
-algebra structure on the integral cohomology H*(X)), obstructions are defined by means of spherical twisting cochains of . In particular, for a given section
on n-skeleton of X, the problem of avoiding the (n+1)th obstruction
to the existence of a section on X
n+1 reduces to solving a system of linear equations with respect to cohomology elements of the groups
Homotopy classification theorems for sections as well as for weak formal maps are given, too. 相似文献
17.
D. M. Smirnov 《Algebra and Logic》2004,43(4):249-257
For integers 1 m < n, a Cantor variety with m basic n-ary operations i and n basic m-ary operations k is a variety of algebras defined by identities k(1(
), ... , m(
)) =
k and i(1(
), ... ,n(
)) = y
i, where
= (x
1., ... , x
n) and
= (y
1, ... , y
m). We prove that interpretability types of Cantor varieties form a distributive lattice, , which is dual to the direct product 1 × 2 of a lattice, 1, of positive integers respecting the natural linear ordering and a lattice, 2, of positive integers with divisibility. The lattice is an upper subsemilattice of the lattice
of all interpretability types of varieties of algebras. 相似文献
18.
Matthew R. Brown 《Journal of Algebraic Combinatorics》2002,15(2):107-125
If a GQ S of order (s, s) is contained in a GQ S of order (s, s
2) as a subquadrangle, then for each point X of S\S the set of points
of S collinear with X form an ovoid of S. Thas and Payne proved that if S=
(4,q),q even, and
is an elliptic quadric for each XS\S,thenS
(5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex. 相似文献
19.
Alexander A. Ivanov 《Journal of Algebraic Combinatorics》1992,1(1):45-69
The sporadic simple group F
2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry
. P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let
be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of
is isomorphic to the corresponding residue in
. We show that in this case
is isomorphic to
. This result realizes a step in classification of the flag-transitive P-geometries and also plays an important role in the characterization of the Fischer–Griess Monster in terms of its 2-local parabolic geometry. 相似文献
20.
Martin Hildebrand 《Journal of Algebraic Combinatorics》1992,1(2):133-150
This paper studies a random walk based on random transvections in SL
n(F
q
) and shows that, given
> 0, there is a constant c such that after n + c steps the walk is within a distance
from uniform and that after n – c steps the walk is a distance at least 1 –
from uniform. This paper uses results of Diaconis and Shahshahani to get the upper bound, uses results of Rudvalis to get the lower bound, and briefly considers some other random walks on SL
n(F
q
) to compare them with random transvections. 相似文献