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This is a combinatorial study of the Poincar e polynomials of iso-typic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials generalize the Kostka-Foulkes polynomials and are q-analogues of Littlewood-Richardson coeecients. The coeecients of two-column Macdonald-Kostka polynomials(More)
We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n, C). Our main results are: • Pieri rules for the Schubert bases of H * (Gr) and H * (Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. • A new combinatorial definition for k-Schur(More)
We present a simple proof of the Littlewood-Richardson rule using a sign-reversing involution, and show that a similar involution provides a com-binatorial proof of the SXP algorithm of Chen, Garsia, and Remmel 2] which computes the Schur function expansion of the plethysm of a Schur function and a power sum symmetric function. The methods of this paper(More)
Level-restricted paths play an important rôle in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijec-tion between Littlewood–Richardson tableaux and rigged configurations is well-behaved with respect to level-restriction and give an explicit characterization of(More)
The X = M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac–Moody algebra. In this paper we prove the X = M conjecture for tensor products of Kirillov–Reshetikhin crystals B 1,s(More)
Expression of mRNA for pituitary adenylate cyclase-activating polypeptide (PACAP) was detected in the cochlea of rats using a reverse transcription-polymerase chain reaction and in situ hybridization. Examination of in situ hybridization demonstrated that cells in the spiral ganglion, and marginal cells in the stria vascularis expressed mRNA for PACAP.(More)