| 21. |
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| 22. |
- Rosengren, Hjalmar, 1972
(författare)
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Felder's Elliptic Quantum Group and Elliptic Hypergeometric Series on the Root System A(n)
- 2011
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Ingår i: International Mathematics Research Notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; :13, s. 2861-2920
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a generalization of elliptic 6 j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of multivariable elliptic hypergeometric series related to the root system A(n). As a consequence, we obtain new biorthogonality relations for such series.
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| 23. |
- Rosengren, Hjalmar, 1972
(författare)
-
Gustafson-Rakha-Type Elliptic Hypergeometric Series
- 2017
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Ingår i: Symmetry Integrability and Geometry-Methods and Applications. - : SIGMA (Symmetry, Integrability and Geometry: Methods and Application). - 1815-0659. ; 13
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Tidskriftsartikel (refereegranskat)abstract
- We prove a multivariable elliptic extension of Jackson's summation formula conjectured by Spiridonov. The trigonometric limit case of this result is due to Gustafson and Rakha. As applications, we obtain two further multivariable elliptic Jackson summations and two multivariable elliptic Bailey transformations. The latter four results are all new even in the trigonometric case.
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| 24. |
- Rosengren, Hjalmar, 1972, et al.
(författare)
-
Harmonic analysis on the SU(2) dynamical quantum group
- 2001
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Ingår i: Acta Applicandae Mathematicae. ; 69, s. 163-220
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Tidskriftsartikel (refereegranskat)abstract
- Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang-Baxter equation, which is precisely the Yang-Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey-Wilson polynomials, and the Haar measure with the Askey-Wilson measure. The discrete orthogonality of the matrix elements yield the orthogonality of q-Racah polynomials (or quantum 6j-symbols). The Clebsch-Gordan coefficients for representations and corepresentations are also identified with q-Racah polynomials. This results in new algebraic proofs of the Biedenharn-Elliott identity satisfied by quantum 6j-symbols.
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| 25. |
- Rosengren, Hjalmar, 1972
(författare)
-
Karlsson-Minton type hypergeometric functions on the root system Cn
- 2003
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Ingår i: Journal of Mathematical Analysis and Applications. ; 281, s. 332-345
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Tidskriftsartikel (refereegranskat)abstract
- We prove a reduction formula for Karlsson-Minton type hypergeometric series on the root system C_n and derive some consequences of this identity. In particular, when combined with a similar reduction formula for A_n, it implies a C_n Watson transformation due to Milne and Lilly.
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| 26. |
- Rosengren, Hjalmar, 1972
(författare)
-
Multivariable Christoffel-Darboux kernels and characteristic polynomials of random Hermitian matrices
- 2006
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Ingår i: Symmetry, Integrability and Geometry: Methods and Applications. ; 2
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Tidskriftsartikel (refereegranskat)abstract
- We study multivariable Christoffel-Darboux kernels, which may be viewed as reproducing kernels for antisymmetric orthogonal polynomials, and also as correlation functions for products of characteristic polynomials of random Hermitian matrices. Using their interpretation as reproducing kernels, we obtain simple proofs of Pfaffian and determinant formulas, as well as Schur polynomial expansions, for such kernels. In subsequent work, these results are applied in combinatorics (enumeration of marked shifted tableaux) and number theory (representation of integers as sums of squares).
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| 27. |
- Rosengren, Hjalmar, 1972
(författare)
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New proofs of determinant evaluations related to plane partitions
- 2012
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Ingår i: Electronic Journal of Combinatorics. - : The Electronic Journal of Combinatorics. - 1077-8926 .- 1097-1440. ; 19:4
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Tidskriftsartikel (refereegranskat)abstract
- We give a new proof of a determinant evaluation due to Andrews, which has been used to enumerate cyclically symmetric and descending plane partitions. We also prove some related results, including a q-analogue of Andrews's determinant.
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| 28. |
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| 29. |
- Rosengren, Hjalmar, 1972, et al.
(författare)
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On a hypergeometric identity of Gelfand, Graev and Retakh
- 2003
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Ingår i: Journal of Computational and Applied Mathematics. ; 160, s. 147-158
-
Tidskriftsartikel (refereegranskat)abstract
- A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of differential equations, is given hypergeometric proofs. As a bonus, several q-analogues can be derived.
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| 30. |
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