共查询到20条相似文献,搜索用时 0 毫秒
1.
James P. Cossey 《Algebras and Representation Theory》2011,14(2):391-402
The Alperin weight conjecture states that if G is a finite group and p is a prime, then the number of irreducible Brauer characters of a group G should be equal to the number of conjugacy classes of p-weights of G. This conjecture is known to be true for the symmetric group S
n
, however there is no explicit bijection given between the two sets. In this paper we develop an explicit bijection between
the p-weights of S
n
and a certain set of partitions that is known to have the same cardinality as the irreducible Brauer characters of S
n
. We also develop some properties of this bijection, especially in relation to a certain class of partitions whose corresponding
Specht modules over fields of characteristic p are known to be irreducible. 相似文献
2.
J. A. Ryan 《Siberian Mathematical Journal》2007,48(2):311-316
A Coxeter system (W, S) is said to be of type K n if the associated Coxeter graph ΓS is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by ΓS. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type K n then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W). 相似文献
3.
In this paper we consider n-poised planar node sets, as well as more special ones, called G C n sets. For the latter sets each n-fundamental polynomial is a product of n linear factors as it always holds in the univariate case. A line ? is called k-node line for a node set \(\mathcal X\) if it passes through exactly k nodes. An (n + 1)-node line is called maximal line. In 1982 M. Gasca and J. I. Maeztu conjectured that every G C n set possesses necessarily a maximal line. Till now the conjecture is confirmed to be true for n ≤ 5. It is well-known that any maximal line M of \(\mathcal X\) is used by each node in \(\mathcal X\setminus M, \)meaning that it is a factor of the fundamental polynomial. In this paper we prove, in particular, that if the Gasca-Maeztu conjecture is true then any n-node line of G C n set \(\mathcal {X}\) is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes. We prove also similar statements concerning n-node or (n ? 1)-node lines in more general n-poised sets. This is a new phenomenon in n-poised and G C n sets. At the end we present a conjecture concerning any k-node line. 相似文献
4.
Erdös et al and Gerencsér et al had shown that in any 2-edge-coloring of K 3n-1, there is a n-matching containing edges with the same color(we call such matching monochromatic matching). In this paper we show that for any 2-edge-coloring of K 3n-1 there exists a monochromatic subgraph H of K 3n-1 which contains exponentially many monochromatic n-matchings. 相似文献
5.
The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g ≥ 2 the order of this group is naturally bounded in terms of g due to a Riemann–Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maximal bound Hurwitz translation surfaces. We study for which g there exist Hurwitz translation surfaces of genus g. 相似文献
6.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
7.
In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ
s
(f
2, f
2, …, f
n
) of the Lie group Sp(n), corresponding to the representation with label (f
1, f
2, ..., f
n
), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f
1, f
2, …, f
n
are all even. 相似文献
8.
W.-D. Richter 《Lithuanian Mathematical Journal》2009,49(1):93-108
For p > 0, the l
n,p
-generalized surface measure on the l
n,p
-unit sphere is studied and used for deriving a geometric measure representation for l
n,p
-symmetric distributions having a density. 相似文献
9.
Let g be the finite dimensional simple Lie algebra of type An, and let U? = U q (g,Λ) and U = U q (g,Q) be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U? for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U? = U q (g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U? = U q (g,Λ) and U = U q (g,Q). 相似文献
10.
V. O. Pekhterev 《Ukrainian Mathematical Journal》2009,61(9):1467-1474
We study the structure of the semigroup OT
n
, which is a unique (up to an isomorphism) R-section of the semigroup T
n
. For this semigroup, we describe Green relations, determine regular and nilpotent elements, describe maximal nilpotent subsemigroups,
and determine the unique irreducible system of generatrices and maximal subsemigroups. 相似文献
11.
Consider a finite group G. A subgroup is called S-quasinormal whenever it permutes with all Sylow subgroups of G. Denote by B
sG
the largest S-quasinormal subgroup of G lying in B. A subgroup B is called S-supplemented in G whenever there is a subgroup T with G = BT and B∩T ≤ B
sG
. A subgroup L of G is called a quaternionic subgroup whenever G has a section A/B isomorphic to the order 8 quaternion group such that L ≤ A and L ∩ B = 1. This article is devoted to proving the following theorem. 相似文献
12.
Gustavo Jasso 《Mathematische Zeitschrift》2016,283(3-4):703-759
We introduce n-abelian and n-exact categories, these are analogs of abelian and exact categories from the point of view of higher homological algebra. We show that n-cluster-tilting subcategories of abelian (resp. exact) categories are n-abelian (resp. n-exact). These results allow to construct several examples of n-abelian and n-exact categories. Conversely, we prove that n-abelian categories satisfying certain mild assumptions can be realized as n-cluster-tilting subcategories of abelian categories. In analogy with a classical result of Happel, we show that the stable category of a Frobenius n-exact category has a natural \((n+2)\)-angulated structure in the sense of Geiß–Keller–Oppermann. We give several examples of n-abelian and n-exact categories which have appeared in representation theory, commutative algebra, commutative and non-commutative algebraic geometry. 相似文献
13.
In this paper, we study the existence of the n-flat preenvelope and the n-FP-injective cover. We also characterize n-coherent rings in terms of the n-FP-injective and n-flat modules. 相似文献
14.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
15.
V. L. Smith 《The Journal of the Operational Research Society》1985,36(4):327-332
Approximation formulae are suggested for the mean and variance of customers in M/E n /s queues. It is shown that the distributions can be approximated by using the mean and variance to fit Gamma functions. A brief comment on the more general E m /E n /s case is given. 相似文献
16.
The j-function j(z) = q−1+ 744 + 196884q + ⋅s plays an important role in many problems. In [7], Zagier, presented an interesting series of functions obtained from the
j-function: jm(ζ) = (j(ζ) – 744)∨T0(m), where T0(m) is the usual m′th normalized weight 0 Hecke operator. In [3], Bruinier et al. show how this series of functions can be used to describe
all meromorphic modular forms on SL2(ℤ). In this note we use these functions and basic notions about modular forms to determine previously unidentified congruence
relations between the coefficients of Eisenstein series and the j-function.
2000 Mathematics Subject Classification: Primary–11B50, 11F03, 11F30
The author thanks the National Science Foundation for their generous support. 相似文献
17.
Yi-Chih Hsieh Mark S. Andersland 《The Journal of the Operational Research Society》1995,46(6):747-752
We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system. 相似文献
18.
QiaoLingXIA YiBingSHEN 《数学学报(英文版)》2004,20(6):1029-1046
In this paper, we reformulate the Euler-Lagrange equations of Willmore surfaces in S^n as the flatness of a family of certain loop algebra-valued 1-forms. Therefore we can give the Weierstrass type representation of conformal Willmore surfaces. We also discuss the relations between conformal Willmore surfaces in S^n and minimal surfaces in constant curvature spaces S^n, R^n, H^n, and prove that some special Willmore surfaces can be derived from minimal surfaces in S^n, R^n, H^n. 相似文献
19.
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D
* is an FC-group, then D is a field. Let M be a maximal subgroup of GL
n
(D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M
n
(D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞. 相似文献
20.
We show that if (p0, p1, ...) is the pn-sequence of a nontrivial algebra with one fundamental operation, then p1 ≥ p0. Moreover, if
, then p1 > 2p0.
Received April 21, 2003; accepted in final form November 28, 2005. 相似文献