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Mathematical Sciences: Combinatorial Methods in Algebra: Coxeter Groups, Hecke Algebras, Young Tableaux, and Symmetric Functions

Mathematical Sciences: Combinatorial Methods in Algebra: Coxeter Groups, Hecke Algebras, Young Tableaux, and Symmetric Functions
数学科学:代数组合方法:Coxeter 群、Hecke 代数、Young Tableaux 和对称函数
批准号:
9119355
负责人:
Mark Haiman
金额:
$4.65万
依托单位国家:
美国
项目类别:
Standard Grant
财政年份:
1992
资助国家:
美国
项目状态:
已结题
起止时间:
1992-01-01 至 1994-08-31

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中文摘要
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英文摘要
The principle investigator will continue his research on problems involving the interaction between combinatorics and algebra. He will focus on two problems. The first concerns new conjectures arising from the principle investigator's application of Kazhdan-Lusztig theory to a problem on combinatorial immanants which assert that certain Hecke algebra virtual characters are polynomials with with non-negative, even unimodal, integer coefficients. A combinatorial approach to these conjectures will be sought, along with combinatorial interpretations of known non-negativity results in Kazhdan-Lusztig theory which now rest on difficult geometric machinery. The second problem concerns the conjecture that the Shur function expansion of Macdonald's symmetric functions are polynomials with non-negative integer coefficients. This project is on the interface between combinatorics and Lie algebra. The principle investigator is concerned with certain polynomials which are combinatorially defined and have deep connections with structures in geometry and representation theory. This work is important both in mathematics and physics.
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EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics
  • 批准号:
    0943745
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $120.01万
  • 财政年份:
    2010
  • 负责人:
    Mark Haiman
  • 依托单位:
Combinatorics of Special Functions in Geometry and Representation Theory
  • 批准号:
    0801262
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $54.0万
  • 财政年份:
    2008
  • 负责人:
    Mark Haiman
  • 依托单位:
Special Meeting: Recent Advances in Combinatorics, CRM Thematic Semester 2007
  • 批准号:
    0603479
  • 项目类别:
    Standard Grant
  • 资助金额:
    $6.85万
  • 财政年份:
    2007
  • 负责人:
    Mark Haiman
  • 依托单位:
EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics
  • 批准号:
    0354321
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $149.95万
  • 财政年份:
    2004
  • 负责人:
    Mark Haiman
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences