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Upper and Lower Bounds for Kazhdan–Lusztig Polynomials

✍ Scribed by F. Brenti

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
221 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis

We give upper and lower bounds for the Kazhdan-Lusztig polynomials of any Coxeter group W . If W is finite we prove that, for any k ≥ 0, the kth coefficient of the Kazhdan-Lusztig polynomial of two elements u, v of W is bounded from above by a polynomial (which depends only on k) in l(v)l(u). In particular, this implies the validity of Lascoux-Schutzenberger's conjecture for all sufficiently long intervals, and gives supporting evidence in favour of the Dyer-Lusztig conjecture.

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