Multivariate $q$-Hypergeometric polynomials as zonal spherical functions over a local field (Various Issues relating to Representation Theory and Non-commutative Harmonic Analysis)
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- Kawamura, Koei
- Department of Mathematics, Faculty of Science, Kyoto University
Bibliographic Information
- Other Title
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- 局所体上の帯球関数として現れる多変数$q$-超幾何多項式 (表現論と非可換調和解析をめぐる諸問題)
- 局所体上の帯球関数として現れる多変数q-超幾何多項式
- キョクショタイ ジョウ ノ タイキュウ カンスウ ト シテ アラワレル タヘンスウ q-チョウキカ タコウシキ
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Abstract
Krawtchouk polynomials are orthogonal polynomials which are defined by the use of the hypergeometric function. They have a group theoretic intepretation as zonal spherical functions on wreath products of symmetric groups (Dunkl, 1976). As a generalization, multivariate Krawtchouk polynomials have an intepretation as zonal spherical functions on complex reflection groups (Mizukawa, 2004). And affine q-Krawtchouk polynomials, one of q-analogues of Krawtchouk polynomials, are also zonal spherical functoins on matrices over a finite field (Delsarte, 1978). In this paper we define new generalizations of Krawtchouk polynomials, that is, ∞-variate Krawtchouk polynomials, multivariate affine q-Krawtchouk polynomials, and ∞-variate affine q-Krawtchouk polynomials. And we show they have also interpretations as zonal spherical functoins on groups concerning finite or non-Archimedean local field.
Journal
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- RIMS Kokyuroku
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RIMS Kokyuroku 2031 15-32, 2017-05
京都大学数理解析研究所
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Details 詳細情報について
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- CRID
- 1050845763139461888
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- NII Article ID
- 120006578967
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- NII Book ID
- AN00061013
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- ISSN
- 18802818
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- HANDLE
- 2433/236738
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- NDL BIB ID
- 028508556
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- Text Lang
- ja
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles