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1.
Eugene Strahov 《Advances in Mathematics》2007,212(1):109-142
Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diagS(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand pair (S(n)×S(n−1),diagS(n−1)). Zonal spherical functions of this Gelfand pair form an orthogonal basis in a larger space of functions on S(n), namely in the space of functions invariant with respect to conjugations by S(n−1). We refer to these zonal spherical functions as normalized generalized characters of S(n). The main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group. The paper gives a Murnaghan-Nakayama type rule, a Frobenius type formula, and an analogue of the determinantal formula for the generalized characters of S(n). 相似文献
2.
Let G be a finite group, H be a proper subgroup of G, and S be a unitary subring of C. The kernel of the restriction map S[Irr(G)] → S[Irr(H)] as a ring homomorphism is studied. As a corollary, the main result in [Isaacs, I. M. and Navarro, G., Injective restriction of characters, Arch. Math., 108, 2017, 437–439] is reproved. 相似文献
3.
We prove that in a finite group of odd order, the number of irreducible quadratic characters is the number of quadratic conjugacy classes. 相似文献
4.
美国哲学家索萨的德性知识论,与儒家的德性论颇有相似之处,因此,建立一种兼具二者资源的联合哲学立场,并非是缘木求鱼。而儒家在这种联合立场的锻造中所能够作出的贡献,便是解释为何德性知识论对于“盖提尔反例”的处理方案,能够在不引入“反思性知识”的前提下,仅仅依赖认知主体的直觉加以执行。说得更具体一点,儒家对于这个问题的解释将诉诸一种对于孔子“正名”论的现代重构,而这种重构亦将高度依赖东汉许慎的“六书”理论。此将说明:在汉语哲学的场域中,亚命题层面上的意义单位的彼此融合,究竟是如何为信念本身的证成提供支撑的。 相似文献
5.
We study asymptotics of an irreducible representation of the symmetric group Sn corresponding to a balanced Young diagram λ (a Young diagram with at most rows and columns for some fixed constant C) in the limit as n tends to infinity. We show that there exists a constant D (which depends only on C) with a property that
6.
We study certain aspects of finite-dimensional non-semisimple symmetric Hopf algebras H and their duals H*. We focus on the set I(H) of characters of projective H-modules which is an ideal of the algebra of cocommutative elements of H*. This ideal corresponds via a symmetrizing form to the projective center (Higman ideal) of H which turns out to be ΛH, where Λ is an integral of H and
is the left adjoint action of H on itself. We describe ΛH via primitive and central primitive idempotents of H. We also show that it is stable under the quantum Fourier transform. Our best results are obtained when H is a factorizable ribbon Hopf algebra over an algebraically closed field of characteristic 0. In this case ΛH is also the image of I(H) under a “translated” Drinfel'd map. We use this fact to prove the existence of a Steinberg-like character. The above ingredients are used to prove a Verlinde-type formula for ΛH. 相似文献
7.
Tomasz Przebinda 《Journal of Functional Analysis》2018,274(5):1284-1305
We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range. 相似文献
8.
在前文工作的基础上,结合MNDO/EHMO分子轨道方法和自然杂化轨道方法,具体计算了CC键和CP键的核自旋偶合常数.计算结果表明,1JCC和1JCP主要由成键原子的轨道杂化作用和键极性这两种结构因素所决定.为从简单价键理论角度解释和计算1JCC和1JCP值提供了简便直观的方法. 相似文献
9.
This work examines the existence of (4q
2,2q
2−q,q
2−q) difference sets, for q=p
f
, where p is a prime and f is a positive integer. Suppose that G is a group of order 4q
2 which has a normal subgroup K of order q such that G/K
≅
C
q
×C
2×C
2, where C
q
,C
2 are the cyclic groups of order q and 2 respectively. Under the assumption that p is greater than or equal to 5, this work shows that G does not admit (4q
2,2q
2−q,q
2−q) difference sets. 相似文献
10.
It is known that characters of irreducible representations of finite Lie algebras can be obtained using the Weyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras of lower rank. By starting from the Weyl character formula, we show that these characters can be re-expressed without referring to Weyl group summations. Some useful technical points are given in detail for the instructive example of G2 Lie algebra. 相似文献