Dual canonical bases and Kazhdan–Lusztig polynomials☆

By Jonathan Brundan. 2005

56 citations recorded by the source corpus.

We derive a formula for the entries of the (unitriangular) transi- tion matrices between the standard monomial and dual canonical bases of the irreducible polynomial representations of Uq(gln) in terms of Kazhdan-Lusztig polynomials.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f61db17d315e560765bd1fa07da2e3068c13aafc

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In Geometry and Topology

Citations in the corpus

On the dual canonical and Kazhdan-Lusztig bases and 3412-, 4231-avoiding permutations (2008, background): “= q(4) 3q!(2) C ′ s[1,5](q)C ′ s[3,6] (q)C ′ s[13,15](q)C ′ s[9,13] (q)C ′ s[4,10](q)C ′ s[14,18] (q).”
A combinatorial approach to functorial quantum slk knot invariants (2007, background): “Is it true that the transformation matrix between the web basis and the canonical basis describes the decomposition of the functors assigned to webs into a direct sum of indecomposable functors? To answer this question one has to improve the categorification presented in the present paper, to includ”
Centers of degenerate cyclotomic Hecke algebras and parabolic category (2006, methodology): “Essentially the same proof as there proves the analogue of this theorem for arbitrary µ, providing one replaces the definition of “standard tableau” used in [BK3] with the less familiar combinatorial notion from [ B1 , (2.2)].”