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    � Generic algebras � Strict Iwahori-Hecke algebras � Representations with Iwahori-fixed vectors � Proof of the Borel-Matsumoto theorem

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    Using the ideas of [Casselman 1980] descended from the Borel-Matsumoto theorem on admissible representations of p-adic reductive groups containing Iwahori-fixed vectors, it is possible to give an easily verifiable sufficient criterion for irreducibility of degenerate principal series. This result is not comparable to irreducibility results such as [Mui?-Shahidi 1998], but is easily proven and easily applied. Let G be a p-adic reductive group, P a minimal parabolic, N its unipotent radical, B the Iwahori subgroup matching P, and K a maximal compact subgroup containing B. As usual, a character ?: P/N ? C is unramified if it is trivial on P ? K. Let ? = ?P be the modular function on P, and ? = ?P = ? 1/2 P the square root of this modular function. 1. Generic algebras Let (W, S) be a Coxeter system, and fix a commutative ring R. We consider S-tuples of pairs (as, bs) of elements of R, subject to the requirement that if s1 = ws2w ?1 for w ? W and s1, s2 ? S, then as1 = as2 and bs1 = bs2. Refer to the constants as, bs as structure constants. Let A be a free R-module with R-basis {Tw: w ? W}. Theorem: Given a Coxeter system (W, S) and structure constants as, bs (s ? S) there is exactly one

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    New Full text for this article was not available? Send a request to the author(s).
    Title : � Generic algebras � Strict Iwahori-Hecke algebras � Representations with Iwahori-fixed vectors � Proof of the Borel-Matsumoto theorem
    Abstract : Using the ideas of [Casselman 1980] descended from the Borel-Matsumoto theorem on admissible representations of p-adic reductive groups containing Iwahori-fixed vectors, it is possible to give an easily verifiable sufficient criterion for irreducibility of degenerate principal series. This result is not comparable to irreducibility results such as [Mui?-Shahidi 1998], but is easily proven and easily applied. Let G be a p-adic reductive group, P a minimal parabolic, N its unipotent radical, B the Iwahori subgroup matching P, and K a maximal compact subgroup containing B. As usual, a character ?: P/N ? C is unramified if it is trivial on P ? K. Let ? = ?P be the modular function on P, and ? = ?P = ? 1/2 P the square root of this modular function. 1. Generic algebras Let (W, S) be a Coxeter system, and fix a commutative ring R. We consider S-tuples of pairs (as, bs) of elements of R, subject to the requirement that if s1 = ws2w ?1 for w ? W and s1, s2 ? S, then as1 = as2 and bs1 = bs2. Refer to the constants as, bs as structure constants. Let A be a free R-module with R-basis {Tw: w ? W}. Theorem: Given a Coxeter system (W, S) and structure constants as, bs (s ? S) there is exactly one
    Subject : unspecified
    Area : Mathematics
    Language : English
    Affiliations : 
    Url : http://www.math.umn.edu/~garrett/m/v/iwahori_fixed.pdf
    Doi : 10.1.1.76.9540

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