13 citations · 13 across the 1 of their papers we have counts for
5 papers
A vector partition function for the multiplicities of sl_k(C)
Sara Billey, Victor Guillemin, Etienne Rassart
We use Gelfand-Tsetlin diagrams to write down the weight multiplicity function for the Lie algebra sl_k(C) (type A_{k-1}) as a single partition function. This allows us to apply kn…
Smoothness of Schubert varieties via patterns in root systems
Sara Billey, Alexander Postnikov
The aim of this article is to present a smoothness criterion for Schubert varieties in generalized flag manifolds in terms of patterns in root systems. We generalize Lakshmib…
Lower bounds for Kazhdan-Lusztig polynomials from patterns
Sara Billey, Tom Braden
We give a lower bound for the value at q=1 of a Kazhdan-Lustig polynomial in a Weyl group W in terms of "patterns''. This is expressed by a "pattern map" from W to W' for any parab…
Maximal singular loci of Schubert varieties in SL(n)/B
Sara C. Billey, Gregory S. Warrington
We give an explicit combinatorial description of the irreducible components of the singular locus of the Schubert variety X_w for any element w in S_n. Our description of the irred…
Kazhdan-Lusztig polynomials for 321-hexagon-avoiding permutations
Sara C. Billey, Gregory S. Warrington
We give a combinatorial formula for the Kazhdan-Lusztig polynomials in the symmetric group when is a 321-hexagon-avoiding permutation. Our formula, which depends on a…