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The equivariant Kazhdan-Lusztig polynomial of a matroid. (English) Zbl 1362.05131
Summary: We define the equivariant Kazhdan-Lusztig polynomial of a matroid equipped with a group of symmetries, generalizing the nonequivariant case. We compute this invariant for arbitrary uniform matroids and for braid matroids of small rank.

MSC:
05E10 Combinatorial aspects of representation theory
05B35 Combinatorial aspects of matroids and geometric lattices
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
05E05 Symmetric functions and generalizations
14N15 Classical problems, Schubert calculus
Software:
SageMath
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References:
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