A recursion formula of the weighted parabolic Kazhdan-Lusztig polynomials. (Q2741043)

The author [in J. Algebra 216, No. 2, 566-599 (1999; Zbl 1058.20008)], introduced weighted parabolic Kazhdan-Lusztig polynomials generalizing the notions of weighted Kazhdan-Lusztig polynomials introduced by \textit{G. Lusztig} [(*) Lie group representations I. College Park/Md. 1982-83, Lect. Notes Math. 1024, 99-111 (1983; Zbl 0537.20019)] and parabolic Kazhdan-Lusztig polynomials introduced by \textit{V. V. Deodhar} [(**) J. Algebra 111, 483-506 (1987; Zbl 0656.22007)]. The author first determines a recursion formula for weighted parabolic Kazhdan-Lusztig polynomials analogous to Lusztig's recursion formula for weighted Kazhdan-Lusztig polynomials [see (*)]. The author further relates the weighted parabolic Kazhdan-Lusztig polynomials to weighted Kazhdan-Lusztig polynomials extending Deodhar's relationship between parabolic Kazhdan-Lusztig polynomials and Kazhdan-Lusztig polynomials [see (**)].NEWLINENEWLINEFor the entire collection see [Zbl 0963.00024].