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arXiv · 1212.3772

On the number of points of the Lusztig nilpotent variety over a finite field

Olivier Schiffmann
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Abstract

In this note we give a closed expression for the number of points over finite fields of the Lusztig nilpotent variety associated to any quiver without edge loops, in terms of Kac's A-polynomial. We conjecture a similar result for quivers in which edge loops are allowed. Finally, we give a formula for the number of points over a finite field of the various stratas of the Lusztig nilpotent variety involved in the geometric realization of the crystal graph.

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Olivier Schiffmann. 2012-12-16. On the number of points of the Lusztig nilpotent variety over a finite field. https://arxiv.org/abs/1212.3772

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