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 $q$-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 $q$-analogues of decomposition numbers of the $v$-Schur algebras for $v$ specialized to a $n$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