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1.
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
2.
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
3.
In this paper, we consider several constructions which from a given B-product *
B
lead to another one
We shall be interested in finding what algebraic properties of the ring
are shared also by the ring
. In particular, for some constructions the rings R
B and
will be isomorphic and therefore have the same algebraic properties. 相似文献
4.
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
5.
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
6.
Elementary Abelian Covers of Graphs 总被引:2,自引:2,他引:0
Aleksander Malnič Dragan Marušič Primož Potočnik 《Journal of Algebraic Combinatorics》2004,20(1):71-97
Let
G
(X) be the set of all (equivalence classes of) regular covering projections of a given connected graph X along which a given group G Aut X of automorphisms lifts. There is a natural lattice structure on
G
(X), where 1 2 whenever 2 factors through 1. The sublattice
G
() of coverings which are below a given covering : X~ X naturally corresponds to a lattice
G
() of certain subgroups of the group of covering transformations. In order to study this correspondence, some general theorems regarding morphisms and decomposition of regular covering projections are proved. All theorems are stated and proved combinatorially in terms of voltage assignments, in order to facilitate computation in concrete applications.For a given prime p, let
G
p
(X)
G
(X) denote the sublattice of all regular covering projections with an elementary abelian p-group of covering transformations. There is an algorithm which explicitly constructs
G
p
(X) in the sense that, for each member of
G
p
(X), a concrete voltage assignment on X which determines this covering up to equivalence, is generated. The algorithm uses the well known algebraic tools for finding invariant subspaces of a given linear representation of a group. To illustrate the method two nontrival examples are included. 相似文献
7.
Niels Jakob Laustsen 《K-Theory》2001,22(3):241-249
Let
Figiel's reflexive Banach space which is not isomorphic to its Cartesian square. We show that the K
0group of the algebra
of continuous, linear operators on
contain a subgroup isomorphic to the group c
00(
) of sequences
rational numbers with z
n=0 eventually. 相似文献
8.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献
9.
For an arbitrary variety
of groups and an arbitrary class
of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) if G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) and N
(respectively, N is a maximal invariant
-subgroup of the group G). 相似文献
10.
The automorphism group of the Barnes-Wall lattice L
m in dimension 2
m
(m ; 3) is a subgroup of index 2 in a certain Clifford group
of structure 2
+
1+2m
. O
+(2m,2). This group and its complex analogue
of structure
.Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for
of degree 2k is spanned by the complete weight enumerators of the codes
, where C ranges over all binary self-dual codes of length 2k; these are a basis if m k - 1. We also give new constructions for L
m and
: let M be the
-lattice with Gram matrix
. Then L
m is the rational part of M
m, and
= Aut(Mm). Also, if C is a binary self-dual code not generated by vectors of weight 2, then
is precisely the automorphism group of the complete weight enumerator of
. There are analogues of all these results for the complex group
, with doubly-even self-dual code instead of self-dual code. 相似文献
11.
V.G. Osmolovskii 《Journal of Mathematical Sciences》2004,122(3):3278-3289
We consider the energy functional of a two-phase elastic medium
with quadratic energy densities
defined for
such that
,where
is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t
-,t
+) of the change of temperature
such that the energy functional has only a minimizer
such that
for
or
such that
t^ + $$
" align="middle" border="0">
. The energy functional has no minimizers
such that
or
if
. We derive two-sided estimates for the numbers
in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles. 相似文献
12.
P. M. Akhmet'ev 《Journal of Mathematical Sciences》2004,119(1):5-9
Pairs B,
of divergence-free vector fields with compact support in
are considered higher-order analog M(B,
c (of order 3) of the Gauss helicity number H(B,
)=
, curl(A)=B; (of order 1) is constructed, which is invariant under volume-preserving diffeomorphisms. An integral expression for M is given. A degree-four polynomial m(B(x1), B(x2),
(
1),
(
2)), x1, x2,
1
2
, is defined, which is symmetric in the first and second pairs of variables separately. M is the average value of m over arbitrary configurations of points. Several conjectures clarifying the geometric meaning of the invariant and relating it to invariants of knots and links are stated. Bibliography: 11 titles. 相似文献
13.
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
14.
Massimo Giulietti Fernanda Pambianco Fernando Torres Emanuela Ughi 《Designs, Codes and Cryptography》2002,25(3):237-246
We point out an interplay between
-Frobenius non-classical plane curves and complete
-arcs in
. A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete
-arcs with parameters
and
being a power of the characteristic. In addition, for q a square, new complete
-arcs with either
and
or
and
are constructed by using certain reducible plane curves. 相似文献
15.
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
16.
Let
and
be groups and let
be an extension of
by
. Given a property
of group compactifications, one can ask whether there exist compactifications
and
of N and K such that the universal
-compactification of G is canonically isomorphic to an extension of
by
. We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties
and then apply this result to the almost periodic and weakly almost periodic compactifications of G. 相似文献
17.
A. I. Budkin 《Algebra and Logic》2000,39(6):363-369
Let
be a class of all groups G for which the normal closure (x)
G
of every element x belongs to a class
.
is a Levi class generated by
. Let
and
0 be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that
and
, and so
and
. It is shown that quasivarieties
and
are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that
is closed under free products if so is
. 相似文献
18.
Stefano Cavallaro 《Algebras and Representation Theory》2000,3(2):175-186
Let
be an Abelian unital C
*-algebra and let
denote its Gelfand spectrum. We give some necessary and sufficient conditions for a nondegenerate representation of
to be unitarily equivalent to a representation in which the elements of
act multiplicatively, by their Gelfand transforms, on a space L
2(
,), where is a positive measure on the Baire sets of
. We also compare these conditions with the multiplicity-free property of a representation. 相似文献
19.
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
20.
Hendrik Grundling 《Acta Appl Math》1997,46(2):107-145
Given an inductive limit group
where each
is locally compact, and a continuous two-cocycle
, we construct a C*-algebra
group algebra
is imbedded in its multiplier algebra
, and the representations of
are identified with the strong operator continuous
of G. If any of these representations are faithful, the above imbedding is faithful. When G is locally compact,
is precisely
, the twisted group algebra of G, and for these reasons we regard
in the general case as a twisted group algebra for G. Applying this construction to the CCR-algebra over an infinite dimensional symplectic space (S,\,B),we realise the regular representations as the representation space of the C*-algebra
, and show that pointwise continuous symplectic group actions on (S,\, B) produce pointwise continuous actions on
, though not on the CCR-algebra. We also develop the theory to accommodate and classify 'partially regular' representations, i.e. representations which are strong operator continuous on some subgroup H of G (of suitable type) but not necessarily on G, given that such representations occur in constrained quantum systems. 相似文献