Notes on Schubert, Grothendieck and Key Polynomials

被引：14
|
作者：
Kirillov, Anatol N. [1 ,2 ,3 ]
机构：
[1] Math Sci Res Inst, Sakyo Ku, Kyoto 6068502, Japan
[2] Kavli Inst Phys & Math Universe IPMU, 5-1-5 Kashiwanoha, Kashiwa, Chiba 2778583, Japan
[3] Natl Res Univ, Higher Sch Econ, Dept Math, 7 Vavilova Str, Moscow 117312, Russia
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2016年 / 12卷
关键词：
plactic monoid and reduced plactic algebras; nilCoxeter and idCoxeter algebras; Schubert; beta-Grothendieck; key and (double) key-Grothendieck; and Di Francesco-Zinn-Justin polynomials; Cauchy's type kernels and symmetric; totally symmetric plane partitions; and alternating sign matrices; noncrossing Dyck paths and (rectangular) Schubert polynomials; multi-parameter deformations of Genocchi numbers of the first and the second types; Gandhi-Dumont polynomials and (staircase) Schubert polynomials; double affine nilCoxeter algebras; ALTERNATING-SIGN MATRICES; SYMMETRY CLASSES; SCHUR-FUNCTIONS; YOUNG TABLEAUX; ALGEBRA; FORMULA; RING;
D O I：
10.3842/SIGMA.2016.034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：57
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