journal article
Open Access
Jan 30, 2024
Kazhdan–Lusztig polynomials of braid matroids
Communications of the American Mathematical Society
Vol. 4
No. 2
pp. 64-79
·
American Mathematical Society (AMS)
Abstract
We provide a combinatorial interpretation of the Kazhdan–Lusztig polynomial of the matroid arising from the braid arrangement of type
A
n
−
1
\mathrm {A}_{n-1}
, which gives an interpretation of the intersection cohomology Betti numbers of the reciprocal plane of the braid arrangement. Moreover, we prove an equivariant version of this result. The key combinatorial object is a class of matroids arising from series-parallel networks. As a consequence, we prove a conjecture of Elias, Proudfoot, and Wakefield on the top coefficient of Kazhdan–Lusztig polynomials of braid matroids, and we provide explicit generating functions for their Kazhdan–Lusztig and
Z
Z
-polynomials.
A
n
−
1
\mathrm {A}_{n-1}
, which gives an interpretation of the intersection cohomology Betti numbers of the reciprocal plane of the braid arrangement. Moreover, we prove an equivariant version of this result. The key combinatorial object is a class of matroids arising from series-parallel networks. As a consequence, we prove a conjecture of Elias, Proudfoot, and Wakefield on the top coefficient of Kazhdan–Lusztig polynomials of braid matroids, and we provide explicit generating functions for their Kazhdan–Lusztig and
Z
Z
-polynomials.
Topics
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References
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Metrics
3
Citations
39
References
Details
- Published
- Jan 30, 2024
- Vol/Issue
- 4(2)
- Pages
- 64-79
- License
- View
Authors
Funding
Vetenskapsrådet
Award: 2018-03968
Cite This Article
Luis Ferroni, Matt Larson (2024). Kazhdan–Lusztig polynomials of braid matroids. Communications of the American Mathematical Society, 4(2), 64-79. https://doi.org/10.1090/cams/28
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