2012 Fiscal Year Final Research Report
Lie theory for alternating sign matrices
| Project/Area Number |
22654004
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
OKADA Soichi 名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIKAWA Masao 琉球大学, 教育学部, 教授 (40243373)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 交代符号行列 / 古典群 / 対称関数 |
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| Research Abstract |
We investigate the structure of the set of half-turn symmetric alternating sign matrices. Also we give a determinantal formula for irreducible spinor representations of the Pin group, and introduce a family of symmetric functions (spinor universal characters) with coefficients in the ring of integers adjoining a new element e with the property e^2 = 1. And we investigate their properties, and describe a combinatorial method for the irreducible decompositions of tensor products and restrictionsinvolving spinor representations of the Pin group.
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