We consider the complement W\WJ of any quotient WJ of a Coxeter system (W,S) and we investigate its algebraic, combinatorial and geometric properties, emphasizing its connection with parabolic Kazhdan–Lusztig theory. In particular, we define two families of polynomials which are the analogues, for the poset W\WJ, of the parabolic Kazhdan–Lusztig and R-polynomials. These polynomials, indexed by elements of W\WJ, have interesting connections with the ordinary Kazhdan–Lusztig and R-polynomials.
Complements of Coxeter group quotients
Sentinelli P.
2015-01-01
Abstract
We consider the complement W\WJ of any quotient WJ of a Coxeter system (W,S) and we investigate its algebraic, combinatorial and geometric properties, emphasizing its connection with parabolic Kazhdan–Lusztig theory. In particular, we define two families of polynomials which are the analogues, for the poset W\WJ, of the parabolic Kazhdan–Lusztig and R-polynomials. These polynomials, indexed by elements of W\WJ, have interesting connections with the ordinary Kazhdan–Lusztig and R-polynomials.File in questo prodotto:
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