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Explicit Formulae for Some Kazhdan–Lusztig R-Polynomials

✍ Scribed by Michela Pagliacci

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
134 KB
Volume
95
Category
Article
ISSN
0097-3165

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✦ Synopsis

We consider the Kazhdan Lusztig R-polynomials, R u, v (q) indexed by permutations u, v'' having particular forms. More precisely, we show that R e, 34 } } } n12 (q) (where e'' denotes the identity permutation) equals, aside from a simple change of variable, a q-analogue of the Fibonacci number, and if two permutations are obtained one from the other by applying two transpositions (one simple, and one not), then the corresponding R-polynomial factors nicely. Our proofs are combinatorial.

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