Irreducible representations of the full linear group
نویسندگان
چکیده
منابع مشابه
Modular irreducible representations of the symmetric group as linear codes
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 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 show the intimate connection Schur functions have with the irreducible polynomial representations of GL(n,C). Following Schur’s thesis, in Section 1, we prove that the characters of these representations are given by Schur functions. In the second section, we elaborate on how a specific combinatorial operation on symmetric functions called plethysm gives the characters of the composition of ...
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Let G be a countable discrete group. Call two subgroups H1 and H2 of G commensurable if H1 ∩H2 has finite index in both H1 and H2. We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the mapping class group on the complex of curves has noncommensurable ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1981
ISSN: 0024-3795
DOI: 10.1016/0024-3795(81)90147-6