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The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field

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Abstract

Let G=GL n (F q ) be the finite general linear group and let M=M n (F q ) be the monoid of all n×n matrices over F q . Let B be a Borel subgroup of G, let W be the subgroup of permutation matrices, and let ℛ⊃W be the monoid of all zero-one matrices which have at most one non-zero entry in each row and each column. The monoid ℛ plays the same role for M that the Weyl group W does for G. In particular there is a length function on ℛ which extends the length function on W and a C-algebra H C (M, B) which includes Iwahori's ‘Hecke algebra’ H C (G, B) and shares many of its properties.

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  1. University of Wisconsin, 53706, Madison, WI, USA

    Louis Solomon

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  1. Louis Solomon
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For Jacques Tits on his sixtieth birthday

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Solomon, L. The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field. Geom Dedicata 36, 15–49 (1990). https://doi.org/10.1007/BF00181463

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