[Cherubino] Quaderni Elettronici del Seminario di Geometria Combinatoria 8E (Maggio 2003), 1--3
Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica

Francesco BRENTI
Kazhdan-lusztig Polynomials, finite geometries and combinatorial invariance (Algebraic Combinatorics Seminars - 3)
(Maggio 2003)

Abstract. Kazhdan-Lusztig polynomials were defined for the first time in 1979, in an inductive and rather complex way, and they are associated with every pair of elements of any Coxeter group. These polynomials play a fundamental role in several branches of mathematics, such as representation theory and geometry of Schubert varieties, and they can be defined in terms of intersection cohomology, or in terms of composition series of Verma modules. Although it is not generally known, these polynomials can be defined also in terms of finite geometries.

In this talk, I will explain this connection/definition and then I will present the solution of a problem proposed by Lusztig in 1980, known as the "combinatorial invariance" problem. More precisely, I will explain a simple, explicit procedure, which can be applied to any partially ordered set, which allows to compute these polynomials.

Author:
Francesco Brenti
Dipartimento di Matematica
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica, 1 - 00133 Roma
e-mail: brenti@mat.uniroma2.it
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