Parabolic Kostka polynomials, quiver varieties, crystal bases and tropicalcombinatorics

抛物线 Kostka 多项式、箭袋变量、晶体基和热带组合

• 批准号: 15340006
• 负责人: KIRILLOV Anatol N.
• 金额: $ 6.53万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340006/
• 关键词: Parabolic Kostka polynomials; Tropical RSK; Amoebas; Torus knots; Virasoro algebra; Nichols-Woronowicz algebras; Schubert Calculus; Flat connections; Parabolic Kostka polynomials; Tropical RSK; Discrete integrable systems; Nichols algebras; We

During 2003-2006 years in the course of the Project "Parabolic Kostka polynomials, quiver varieties, crystal bases and tropical combinatorics", the members of the Project have published about 25 papers in the leading mathematical journals, have organized and attended several International and Domestic Conferences and Workshops, participated regularly in the joint discussions and collaboration.The main event of 2003 year term of the Project "Parabolic Kostka polynomials, quiver varieties, crystal bases and tropical combinatorics" was the "International Workshop on Quantum Cohomology" to be held during June 16-19, 2003 at RIMS, Kyoto University, and organized by A.N.Kirillov and M.Guest (Tokyo Metropolitan University). The Workshop collected several leading specialists in the field such as Profs. H.Nakajima (Kyodai), K.Saito (RIMS), B.Kim (S.Korea), A.-L.Mare (Canada), A.Buch (Sweden), as well as many (about 50) domestic participants.The main event of 2004 year term of the Project "Parab … More olic Kostka polynomials, quiver varieties, crystal bases and tropical combinatorics" was the International Workshop "Tropical algebraic geometry and tropical combinatorics" carried out August 8-22, RIMS, Kyoto University, and organized by A.N.Kirillov and M.Noumi. The Workshop collected several leading specialist in "Tropical Mathematics" such as Profs. A.Knutson (UC Berkeley, USA), E.Miller (Univ. of Minnesota, USA), G.Mikhalkin (Toronto Univ., Canada), D.Speyer (UC Berkeley, USA), O.Viro (Uppsala Univ., Sweden), M.Kashiwara (RIMS), M.Okado (Osaka), Y.Yamada (Kobe), as well as many (near 60) domestic participants.The both Workshops were recognized to be successful and gave rise to notable interest to Tropical Mathematics and Quantum Cohomology in Japan.In the body of the Project, A.N.Kirillov attended as invited speaker the International Workshop "Combinatorics, Special Functions and Physics, 2004" held August 2-4, Nankai Univ., China, and several domestic Conferences.Part of basic results about parabolic Kostka polynomials obtained by A.N.Kirillov in the body of project, has been published in the Publications of RIMS, vol. 40. In particular, this paper contains a proof of the so-called Generalized Saturation Conjecture, as well as proofs of several new interesting properties of parabolic Kostka polynomials, Schur functions and so on.Several important results about connections between Schubert Calculus and non-commutative differential calculus have been obtained and published by A.N.Kirillov and T.Maeno. In particular, we described the algebra generated by flat connections for some noncommutative algebraic varieties, and prove Monk formula for noncommutative B_n Schubert polynomials. Less

在2003年至2006年的过程中，在项目“抛物面Kostka多项式，Quiver品种，水晶基础和热带组合主义者”的过程中，该项目的成员在领先的数学期刊上发表了大约25篇论文，在主要的数学期刊上进行了组织，并参加了几个国际和家庭活动，并参与了共同的活动，并参与了共同的活动。 Kostka多项式，Quiver品种，晶体碱和热带组合是在2003年6月16日至19日在京都大学RIMS，由A.N.Kirilov和M.Guest（Tokyo Metropolititan University）组织的“国际量子同谋国际研讨会”。研讨会收集了该领域的几位领先专家，例如教授。 H.Nakajima（Kyodai），K.Saito（RIMS），B.Kim（S.Korea），A.-L.Mare（加拿大），A.Buch（瑞典）以及许多（约50名）国内参与者。研讨会“热带代数几何和热带组合学”于8月8日至22日，京都大学轮辋，由A.N.组织Kirillov和M. Noumi。该研讨会收集了“热带数学”（例如教授）领域的几位领先专家。 A.Knnutson（美国加州大学伯克利分校），E.Miller（美国明尼苏达州大学），G.Mikhalkin（加拿大多伦多大学），D.Speyer（UC Berkeley，USA），O.Viro（U.Viro（Upsala Univ。）就像许多（接近60个）的国内参与者一样。这两个研讨会都被认为是成功的，并引起了日本热带数学和量子同谋的显着兴趣。在该项目的主体中，Kirilov作为邀请演讲者参加了国际研讨会。 A.N. Kirilov在项目主体中获得的抛物线科斯特卡多项式已发表在Rims的出版物中，第1卷。 40。特别是，本文包含了所谓的广义饱和构想的证明，以及证明了抛物线核心Kostka多项式，Schur功能等几种新有趣的特性。有关Schubert calculus和非交通型差异化合物之间的联系的重要结果，已通过A.N.Kirirov获得和发表。特别是，我们描述了某些非共同代数品种的平坦连接产生的代数，并证明了非交通b_n schubert多项式的和尚公式。较少的

项目成果

Wonderful Amoebas

奇妙的阿米巴原虫

• 发表时间: 2006
• 期刊: Sugaku 58
• 作者: Kirillov.A.N.;T.Maeno
• 通讯作者: T.Maeno

On some quadratic algebras, II

关于一些二次代数，II

• 期刊: Preprint (submitted)
• 作者: Kirillov.A.N.;van Diejen F.;Hiroyuki Ochiai;Kirillov.A.N.
• 通讯作者: Kirillov.A.N.

Elementary Askey-Wilson functions

基本 Askey-Wilson 函数

• 期刊: (submitted)
• 作者: Kirillov.A.N.;van Diejen F.
• 通讯作者: van Diejen F.

On some noncommutative algebras related with K-theory of flag varieties

与旗簇K理论相关的一些非交换代数

• 发表时间: 2005
• 期刊: International Research Mathematical Notices 60
• 作者: Kirillov.A.N.;T.Maeno
• 通讯作者: T.Maeno

Torus knot and minimal model

环面结和最小模型

• 发表时间: 2003
• 期刊: Physics Letters B 575
• 作者: Kirillov.A.N.;K.Hikami
• 通讯作者: K.Hikami