248 research outputs found
The cycle enumerator of unimodal permutations
We give a generating function for the number of unimodal permutations with a
given cycle structure.Comment: 7 pages, LaTe
Superization and (q,t)-specialization in combinatorial Hopf algebras
We extend a classical construction on symmetric functions, the superization
process, to several combinatorial Hopf algebras, and obtain analogs of the
hook-content formula for the (q,t)-specializations of various bases. Exploiting
the dendriform structures yields in particular (q,t)-analogs of the
Bjorner-Wachs q-hook-length formulas for binary trees, and similar formulas for
plane trees.Comment: 30 page
Canonical bases of q-deformed Fock spaces
We define a canonical basis of the -deformed Fock space representation of
the affine Lie algebra \glchap_n. We conjecture that the entries of the
transition matrix between this basis and the natural basis of the Fock space
are -analogues of decomposition numbers of the -Schur algebras for
specialized to a th root of unity.Comment: 7 pages, LaTe
Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials
We show that the Littlewood-Richardson coefficients are values at 1 of
certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups.
These q-analogues of Littlewood-Richardson multiplicities coincide with those
previously introduced in terms of ribbon tableaux.Comment: 51 pages, 10 Figures, Minor corrections and typos, and some new
comments concerning Soergel's character formula for tilting module
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