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## Mirabolic affine Grassmannian and character sheaves

Selecta Mathematica, New Series. 2009. Vol. 14. No. 3-4. P. 607-628.
Ginzburg V., Travkin R., Finkelberg M. V.

We compute the Frobenius trace functions of mirabolic character sheaves defined over a finite field. The answer is given in terms of the character values of general linear groups over the finite field, and the structure constants of multiplication in the mirabolic Hall–Littlewood basis of symmetric functions, introduced by Shoji.