163 research outputs found
Deformed Kazhdan-Lusztig elements and Macdonald polynomials
We introduce deformations of Kazhdan-Lusztig elements and specialised
nonsymmetric Macdonald polynomials, both of which form a distinguished basis of
the polynomial representation of a maximal parabolic subalgebra of the Hecke
algebra. We give explicit integral formula for these polynomials, and
explicitly describe the transition matrices between classes of polynomials. We
further develop a combinatorial interpretation of homogeneous evaluations using
an expansion in terms of Schubert polynomials in the deformation parameters.Comment: major revision, 29 pages, 22 eps figure
Factorization of the canonical bases for higher level Fock spaces
The level l Fock space admits canonical bases G_e and G_\infty. They
correspond to U_{v}(hat{sl}_{e}) and U_{v}(sl_{\infty})-module structures. We
establish that the transition matrices relating these two bases are
unitriangular with coefficients in N[v]. Restriction to the highest weight
modules generated by the empty l-partition then gives a natural quantization of
a theorem by Geck and Rouquier on the factorization of decomposition matrices
which are associated to Ariki-Koike algebras.Comment: The last version generalizes and proves the main conjecture of the
previous one. Final versio
Hecke Algebra Actions on the Coinvariant Algebra
Two actions of the Hecke algebra of type A on the corresponding polynomial
ring are studied. Both are deformations of the natural action of the symmetric
group on polynomials, and keep symmetric functions invariant. We give an
explicit description of these actions, and deduce a combinatorial formula for
the resulting graded characters on the coinvariant algebra.Comment: 21 pages; final form, to appear in the Journal of Algebr
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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