We give an explicit combinatorial product formula for the parabolic Kazhdan–Lusztig polynomials of the tight quotients of the symmetric group. This formula shows that these polynomials are always either zero or a monic power of q and implies the main result in [F. Brenti, Kazhdan–Lusztig and R-polynomials, Young’s lattice, and Dyck partitions, Pacific J. Math. 207 (2002) 257–286] on the parabolic Kazhdan–Lusztig polynomials of the maximal quotients. The formula depends on a new class of superpartitions.
Kazhdan--Lusztig polynomials, tight quotients and Dyck superpartitions / Brenti, F.; Incitti, F.; Marietti, Mario. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - STAMPA. - 47:(2011), pp. 589-614. [10.1016/j.aam.2011.02.002]
Kazhdan--Lusztig polynomials, tight quotients and Dyck superpartitions
MARIETTI, Mario
2011-01-01
Abstract
We give an explicit combinatorial product formula for the parabolic Kazhdan–Lusztig polynomials of the tight quotients of the symmetric group. This formula shows that these polynomials are always either zero or a monic power of q and implies the main result in [F. Brenti, Kazhdan–Lusztig and R-polynomials, Young’s lattice, and Dyck partitions, Pacific J. Math. 207 (2002) 257–286] on the parabolic Kazhdan–Lusztig polynomials of the maximal quotients. The formula depends on a new class of superpartitions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
