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The Kazhdan–Lusztig polynomial of a matroid.
- Source :
-
Advances in Mathematics . Aug2016, Vol. 299, p36-70. 35p. - Publication Year :
- 2016
-
Abstract
- 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 Poincaré polynomials. We also introduce a q -deformation of the Möbius 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 299
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 118151094
- Full Text :
- https://doi.org/10.1016/j.aim.2016.05.005