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Notes on Schubert, Grothendieck and Key Polynomials
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Notes on Schubert, Grothendieck and Key Polynomials
Інший ID:
2010 Mathematics Subject Classification: 05E05; 05E10; 05A19
DOI:10.3842/SIGMA.2016.034
DOI:10.3842/SIGMA.2016.034
Посилання:
Notes on Schubert, Grothendieck and Key Polynomials / A.N. Kirillov // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 72 назв. — англ.
Підтримка:
A bit of history. Originally these notes have been designed as a continuation of [17]. The main
purpose was to extend the methods developed in [18] to obtain by the use of plactic algebra,
a noncommutative generating function for the key (or Demazure) polynomials introduced by
A. Lascoux and M.-P. Sch¨utzenberger [53]. The results concerning the polynomials introduced
in Section 4, except the Hecke–Grothendieck polynomials, see Definition 4.6, has been presented
in my lecture-courses “Schubert Calculus” and have been delivered at the Graduate School
of Mathematical Sciences, the University of Tokyo, November 1995 – April 1996, and at the
Graduate School of Mathematics, Nagoya University, October 1998 – April 1999. I want to
thank Professor M. Noumi and Professor T. Nakanishi who made these courses possible. Some
early versions of the present notes are circulated around the world and now I was asked to
put it for the wide audience. I would like to thank Professor M. Ishikawa (Department of
Mathematics, Faculty of Education, University of the Ryukyus, Okinawa, Japan) and Professor
S. Okada (Graduate School of Mathematics, Nagoya University, Nagoya, Japan) for valuable
comments. My special thanks to the referees for very careful reading of a preliminary version of
the present paper and many valuable remarks, comments and suggestions.
Дата:
2016
Переглядів:
629
Завантажень:
277
Анотація:
We introduce common generalization of (double) Schubert, Grothendieck, Demazure, dual and stable Grothendieck polynomials, and Di Francesco-Zinn-Justin polynomials. Our approach is based on the study of algebraic and combinatorial properties of the reduced rectangular plactic algebra and associated Cauchy kernels.
