Grothendieck polynomials

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  • Given a permutation w ∈ Sn , we consider a determinantal ideal Iw whose generators are certain minors in the generic n × n matrix (filled with independent variables). Using ‘multidegrees’ as simple algebraic substitutes for torus-equivariant cohomology classes on vector spaces, our main theorems describe, for each ideal Iw : • variously graded multidegrees and Hilbert series in terms of ordinary and double Schubert and Grothendieck polynomials;

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  • Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Factorial Grothendieck Polynomials...

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  • This volume contains the Proceedings of the Workshop "Physics and Combinatorics" held at the Graduate School of Mathematics, Nagoya University, Japan, during August 21-26, 2000. The workshop organizing committee consisted of Kazuhiko Aomoto, Fumiyasu Hirashita, Anatol Kirillov, Ryoichi Kobayashi, Akihiro Tsuchiya, and Hiroshi Umemura.

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  • We consider a specialization of an untwisted quantum affine algebra of type ADE at a nonzero complex number, which may or may not be a root of unity. The Grothendieck ring of its finite dimensional representations has two bases, simple modules and standard modules. We identify entries of the transition matrix with special values of “computable” polynomials, similar to Kazhdan-Lusztig polynomials. At the same time we “compute” q-characters for all simple modules. The result is based on “computations” of Betti numbers of graded/cyclic quiver varieties.

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