[Cherubino] Quaderni Elettronici del Seminario di Geometria Combinatoria 10E (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-1sn sn-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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