Matrix Valued Classical Pairs Related to Compact Gelfand Pairs of Rank One
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Matrix Valued Classical Pairs Related to Compact Gelfand Pairs of Rank One
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| Creator |
Maarten van Pruijssen
Román, P. |
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| Description |
We present a method to obtain infinitely many examples of pairs (W,D) consisting of a matrix weight W in one variable and a symmetric second-order differential operator D. The method is based on a uniform construction of matrix valued polynomials starting from compact Gelfand pairs (G,K) of rank one and a suitable irreducible K-representation. The heart of the construction is the existence of a suitable base change Ψ₀. We analyze the base change and derive several properties. The most important one is that Ψ₀ satisfies a first-order differential equation which enables us to compute the radial part of the Casimir operator of the group G as soon as we have an explicit expression for Ψ0. The weight W is also determined by Ψ₀. We provide an algorithm to calculate Ψ₀ explicitly. For the pair (USp(2n),USp(2n−2)×USp(2)) we have implemented the algorithm in GAP so that individual pairs (W,D) can be calculated explicitly. Finally we classify the Gelfand pairs (G,K) and the K-representations that yield pairs (W,D) of size 2×2 and we provide explicit expressions for most of these cases.
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| Date |
2019-02-09T11:22:55Z
2019-02-09T11:22:55Z 2014 |
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| Type |
Article
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| Identifier |
Matrix Valued Classical Pairs Related to Compact Gelfand Pairs of Rank One / Maarten van Pruijssen , P. Román // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 40 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 22E46; 33C47 DOI: http://dx.doi.org/10.3842/SIGMA.2014.113 http://dspace.nbuv.gov.ua/handle/123456789/146404 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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