Quaderni Elettronici del Seminario di Geometria Combinatoria10E (Maggio 2003), 1--13
Università degli Studi di Roma "La Sapienza" - Dipartimento di
Matematica
Mario MARIETTI Kazdhan-Lusztig polynomials for boolean elements in linear Coxeter systems
(Algebraic Combinatorics Seminars - 5)
(Maggio 2003)
Abstract. Kazhdan-Lusztig polynomials have been proven to play an
important role in different fields. Despite this, there still few explicit
formulas for them. Here we give closed product formulas for the
R-polynomials and for the Kazhdan-Lusztig polynomials when they are
indexed by Boolean elements. Boolean elements are elements smaller than a
reflection that admits a reduced expression of the form
s1...sn-1snsn-1...s1 (si in
S, si different from sj if
i is different from j). Then we provide several applications
of this result concerning the combinatorial invariance of Kazhdan-Lusztig
polynomials, the classification of the pairs (u, v) with
u < v, the Kazhdan-Lusztig elements and the intersection
homology Poincaré polynomials of the Schubert varieties.
Author:
Mario Marietti
Dipartimento di Matematica
Università di Roma "La Sapienza"
P.le Aldo Moro, 5 - 00185 Roma
e-mail:
marietti@mat.uniroma1.it
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