Geodesic
Equivariant Kazhdan–Lusztig theory of paving matroids
Karn, Trevor1 ; Nasr, George D.2 ; Proudfoot, Nicholas2 ; Vecchi, Lorenzo3
1 University of Minnesota School of Mathematics Minneapolis MN 55455 (USA)
2 University of Oregon Department of Mathematics Eugene OR 97403 (USA)
3 Universitá di Bologna Dipartimento di Matematica Bologna 40126 (Italy)
Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 677-688

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We study the way in which equivariant Kazhdan–Lusztig polynomials, equivariant inverse Kazhdan–Lusztig polynomials, and equivariant Z-polynomials of matroids change under the operation of relaxation of a collection of stressed hyperplanes. This allows us to compute these polynomials for arbitrary paving matroids, which we do in a number of examples, including various matroids associated with Steiner systems that admit actions of Mathieu groups.

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DOI : 10.5802/alco.281
Classification : 05B35, 20C15
Keywords: Paving matroids, Kazhdan–Lusztig, characters of groups

Karn, Trevor 1 ; Nasr, George D. 2 ; Proudfoot, Nicholas 2 ; Vecchi, Lorenzo 3

1 University of Minnesota School of Mathematics Minneapolis MN 55455 (USA)
2 University of Oregon Department of Mathematics Eugene OR 97403 (USA)
3 Universitá di Bologna Dipartimento di Matematica Bologna 40126 (Italy)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Equivariant {Kazhdan{\textendash}Lusztig} theory of paving matroids},
     journal = {Algebraic Combinatorics},
     pages = {677--688},
     publisher = {The Combinatorics Consortium},
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     doi = {10.5802/alco.281},
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Karn, Trevor; Nasr, George D.; Proudfoot, Nicholas; Vecchi, Lorenzo. Equivariant Kazhdan–Lusztig theory of paving matroids. Algebraic Combinatorics, Tome 6 (2023) no. 3, pp. 677-688. doi: 10.5802/alco.281

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