منابع مشابه
Symmetric Cyclotomic Hecke Algebras
In this paper we prove that the generic cyclotomic Hecke algebras for imprimitive complex reeection groups are symmetric over any ring containing inverses of the parameters. For this we show that the determinant of the Gram matrix of a certain canonical sym-metrizing form introduced in 3] is a unit in any such ring. On the way we show that the Ariki-Koike bases of these algebras are also quasi-...
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At the 1991 West Coast Number Theory Conference, Emma Lehmer asked for proofs of the formulas on semi-symmetric cyclotomic sums that appeared without proof in D. H. Lehmer's last notebook. This note is the result. Furthermore, we show how to determine signs which Lehmer had left ambiguous. Classical cyclotomy defined the cyclotomic classes of degree e and prime conductor p = ef + 1 to be (1) C ...
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we characterize strictly diagonal type of embeddings offinitary symmetric groups in terms of cardinality and the characteristic. namely, we prove thefollowing.let $kappa$ be an infinite cardinal. if$g=underset{i=1}{stackrel{infty}bigcup} g_i,$ where $ g_i=fsym(kappa n_i)$,$(h=underset{i=1}{stackrel{infty}bigcup}h_i, $ where $ h_i=alt(kappa n_i) ), $ is a group of strictly diagonal type and$xi=(...
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We construct an explicit generating sets Fn and F̃n of the alternating and the symmetric groups, which make the Cayley graphs C(Alt(n), Fn) and C(Sym(n), F̃n) a family of bounded degree expanders for all sufficiently large n. These expanders have many applications in the theory of random walks on groups and other areas of mathematics. A finite graph Γ is called an ǫ-expander for some ǫ ∈ (0, 1), ...
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In this thesis we study the ordinary and the modular representation theory of the symmetric group. In particular we focus our work on different important open questions in the area. 1. Foulkes’ Conjecture In Chapter 2 we focus our attention on the long standing open problem known as Foulkes’ Conjecture. We use methods from character theory of symmetric groups to determine new information on the...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2005
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.02.031