Equivariant Kazhdan–Lusztig polynomials of q-niform matroids
Algebraic Combinatorics, Volume 2 (2019) no. 4, p. 613-619

We study q-analogues of uniform matroids, which we call q-niform matroids. While uniform matroids admit actions of symmetric groups, q-niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan–Lusztig polynomial of a q-niform matroid is the unipotent q-analogue of the equivariant Kazhdan–Lusztig polynomial of the corresponding uniform matroid, thus providing evidence for the positivity conjecture for equivariant Kazhdan–Lusztig polynomials.

Received : 2018-09-01
Revised : 2019-01-18
Accepted : 2019-01-14
Published online : 2019-08-01
DOI : https://doi.org/10.5802/alco.59
Classification:  05B35,  20C33
Keywords: Kazhdan–Lusztig polynomial, matroid, unipotent representation
@article{ALCO_2019__2_4_613_0,
     author = {Proudfoot, Nicholas},
     title = {Equivariant Kazhdan--Lusztig polynomials of $q$-niform matroids},
     journal = {Algebraic Combinatorics},
     publisher = {MathOA foundation},
     volume = {2},
     number = {4},
     year = {2019},
     pages = {613-619},
     doi = {10.5802/alco.59},
     language = {en},
     url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_4_613_0}
}
Equivariant Kazhdan–Lusztig polynomials of $q$-niform matroids. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 613-619. doi : 10.5802/alco.59. https://alco.centre-mersenne.org/item/ALCO_2019__2_4_613_0/

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