Irreducible representations of the generalized symmetric group Bmn
نویسندگان
چکیده
منابع مشابه
Irreducible Representations of the Symmetric Group
We construct the Specht modules and prove that they completely characterize the irreducible representations of the symmetric group. We will prove certain properties of these representations using combinatorial tools (such as calculating the dimension using Hook’s length formula). Only an introductory knowledge of group theory and linear algebra will be assumed and representation theory concepts...
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The intent of this paper is to give the reader, in a general sense, how to go about finding irreducible representations of the Symmetric Group Sn. While I would like to be thorough toward this end, I fear we must assume some results from Wedderburn Theory that will be given without proof because although they are important, proving and discussing these results is not in the scope of this paper....
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We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group. It shows that Specht’s approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen’s approach to the modular irreducible representations using symmetrized standard bideterminants. The unified method, using symmetrized Specht pol...
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We compute the dimension of some irreducible representations of the sym metric groups in characteristic ρ (Theorem 2). The representations considered here are associated with Young diagrams m : πΐχ > m 2 > ... > m/ such that πΐχ — mi < (jp — I). The formula is based on a variant of Verlinde's formula which computes some tensor product multiplicities of indecomposable modules for GLi(¥p), as it...
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We establish the existence of an irreducible representation of An whose dimension does not occur as the dimension of an irreducible representation of Sn, and vice versa. This proves a conjecture by Tong-Viet. The main ingredient in the proof is a result on large prime factors in short intervals.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1987
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500006613