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- Mark Shimozono
- 1998

Answering a question of Kuniba, Misra, Okado, Takagi, and Uchi-yama, it is shown that certain Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent matrices.

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)

We describe the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen. We place this algorithm in the context of Haiman's mixed and left-right insertion algorithms and extend it to colored words. It follows easily from this description that total color of a colored word maps to the sum of the spins of a pair of 2-ribbon tableaux. Various… (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)

Creation operators are given for the three distinguished bases of the type BCD universal character ring of Koike and Terada yielding an elegant way of treating computations for all three types in a unified manner. Deformed versions of these operators create symmetric function bases whose expansion in the universal character basis, has polynomial… (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)

Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases. Conjecturally these poly-nomials coincide with the Poincaré polynomials of isotypic components of certain graded GL(n)-modules supported… (More)