Journal
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
Volume 53, Issue 6, Pages 1501-1544Publisher
SOC MATHEMATIQUE FRANCE
DOI: 10.24033/asens.2452
Keywords
-
Categories
Ask authors/readers for more resources
We give a closed expression for the number of points over finite fields of the Lusztig nilpotent variety associated to any quiver, in terms of Kac's A-polynomials. When the quiver has 1-loops or oriented cycles, there are several possible variants of the Lusztig nilpotent variety, and we provide formulas for the point count of each. This involves nilpotent versions of the Kac A-polynomial, which we introduce and for which we give a closed formula similar to Hua's formula for the usual Kac A-polynomial. Finally we compute the number of points over a finite field of the various strata of the Lusztig nilpotent variety involved in the geometric realization of the crystal graph.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available