2011 Fiscal Year Final Research Report
Multivariate orthogonal polynomials on finite groups and their q-analogues
| Project/Area Number |
21740032
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | 防衛大学校 |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 表現論 / 代数的組合せ論 / 球関数 / 超幾何関数 / ヘッケ環 |
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| Research Abstract |
In this study, I dealt with the special functions arising from finite groups or their q-analogues. As results, I obtained the complete description of the spherical functions of a certain Gelfand pair which is generalization of the Gelfand pair(S_2n, H_n), a necessary and sufficient condition of orthogonal properties of multivariate Krawtchouk polynomials, and a formulae of the character of the symmetric groups. Furthermore I applied these results on finite homogenous spaces as stochastic spaces and obtained a generalization of classical Frobenius-Schur theorem.
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