Geodesic
A GRAPHICAL DESCRIPTION OF (Dn,An−1) KAZHDAN–LUSZTIG POLYNOMIALS
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 313-340

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DOI

We give an easy diagrammatical description of the parabolic Kazhdan–Lusztig polynomials for the Weyl group Wn of type Dn with parabolic subgroup of type An and consequently an explicit counting formula for the dimension of morphism spaces between indecomposable projective objects in the corresponding category . As a by-product we categorify irreducible Wn-modules corresponding to the pairs of one-line partitions. Finally, we indicate the motivation for introducing the combinatorics by connections to the Springer theory, the category of perverse sheaves on isotropic Grassmannians, and to the Brauer algebras, which will be treated in two subsequent papers of the second author.
DOI : 10.1017/S0017089512000547
Mots-clés : 17B10, 16G10, 05E15 
LEJCZYK, TOBIAS; STROPPEL, CATHARINA. A GRAPHICAL DESCRIPTION OF (Dn,An−1) KAZHDAN–LUSZTIG POLYNOMIALS. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 313-340. doi: 10.1017/S0017089512000547
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     title = {A {GRAPHICAL} {DESCRIPTION} {OF} {(Dn,An\ensuremath{-}1)} {KAZHDAN{\textendash}LUSZTIG} {POLYNOMIALS}},
     journal = {Glasgow mathematical journal},
     pages = {313--340},
     year = {2013},
     volume = {55},
     number = {2},
     doi = {10.1017/S0017089512000547},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000547/}
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