Abstract
In this paper we verify a prediction of the Langlands-Lusztig program in the special case of the algebra of double cosets ( K(F q)β GL n(F q) K(F q) ), where K is the fixed point subgroup of an involution on GL n (see Conjecture 3.6 and Example 7 of [G]). We calculate the dimension of the algebra by computing the number of K( F q )-conjugacy classes in the space GL n(F q)) K(F q) . We compare this dimension with the size of the set parametrizing representations of the double coset algebra, defined in terms of perverse sheaves on the flag variety. These numbers turn out to be the same.
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