The Kazhdan-Lusztig polynomial of a matroid
By Ben Elias, Nicholas Proudfoot, Max Wakefield. 2014
90 citations recorded by the source corpus.
We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always non-negative, and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology Poincare polynomials. We also introduce a q-deformation of the Mobius algebra of M, and use our polynomials to define a special basis for this deformation, analogous to the canonical basis of the Hecke algebra. We conjecture that the structure coefficients for multiplication in this special basis are non-negative, and we verify this conjecture in numerous examples.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8fbf6ef0443a7c0c0055fc25527f3fec09844c3d
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In Discrete Mathematics and Combinatorics
- June Huh
- Botong Wang
- Nicholas Proudfoot
- Jacob P. Matherne
- Tom Braden
- Federico Ardila
- Eric Katz
- Petter Brand'en
In Geometry and Topology
- June Huh
- Botong Wang
- Nicholas Proudfoot
- Tom Braden
- Jacob P. Matherne
- Federico Ardila
- Eric Katz
- Paolo Aluffi
In Mathematical Physics
- Jacob P. Matherne
- June Huh
- Nicholas Proudfoot
- Tom Braden
- I. Losev
- P. Fiebig
- Geordie Williamson
- Timo Richarz
Citations in the corpus
- A semi-small decomposition of the Chow ring of a matroid (2020, background): “The image of XA in P (F) is the projective reciprocal plane, which is singular in general, and its intersection cohomology groups are closely related to the Kazhdan–Lusztig polynomial of M (see [14]).”