| 11. |
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| 12. |
- Rosengren, Hjalmar, 1972
(författare)
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An elliptic determinant transformation
- 2005
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Ingår i: M. Noumi and K. Takasaki (eds.), Elliptic Integrable Systems. ; , s. 241-246
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 13. |
- Rosengren, Hjalmar, 1972
(författare)
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An Izergin-Korepin-type identity for the 8VSOS model, with applications to alternating sign matrices
- 2009
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Ingår i: Advances in Applied Mathematics. - : Elsevier BV. - 0196-8858 .- 1090-2074. ; 43:2, s. 137-155
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Tidskriftsartikel (refereegranskat)abstract
- We obtain a new expression for the partition function of the 8VSOS model with domain wall boundary conditions, which we consider to be the natural extension of the Izergin-Korepin formula for the six-vertex model. As applications, we find dynamical (in the sense of the dynamical Yang-Baxter equation) generalizations of the enumeration and 2-enumeration of alternating sign matrices. The dynamical enumeration has a nice interpretation in terms of three-colourings of the square lattice.
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| 14. |
- Rosengren, Hjalmar, 1972, et al.
(författare)
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Continuous Hahn functions as Clebsch-Gordan coefficients
- 2005
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Ingår i: M. E. H. Ismail and E. Koelink (eds.), Theory and Applications of Special Functions - A Volume Dedicated to Mizan Rahman. ; , s. 221-284
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Konferensbidrag (refereegranskat)
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| 15. |
- Rosengren, Hjalmar, 1972
(författare)
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Determinantal elliptic Selberg integrals
- 2020
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Ingår i: Seminaire Lotharingien de Combinatoire. - 1286-4889. ; 81
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Tidskriftsartikel (refereegranskat)abstract
- The classical Selberg integral contains a power of the Vandermonde determinant. When that power is chosen to be a square, it is easy to prove Selberg's identity by interpreting it as a determinant of one-variable integrals. We give similar proofs of summation and transformation formulas for continuous and discrete elliptic Selberg integrals. In the continuous case, the same proof was given previously by Noumi. Special cases of the resulting identities have found applications in combinatorics.
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| 16. |
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| 17. |
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| 18. |
- Rosengren, Hjalmar, 1972
(författare)
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Elliptic hypergeometric functions
- 2020
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Ingår i: Lectures on Orthogonal Polynomials and Special Functions. Howard S. Cohl and Mourad E. H. Ismail (red.). - : Cambridge University Press. - 9781108908993 ; , s. 213-279
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Bokkapitel (refereegranskat)abstract
- The purpose of this chapter is to give an elementary introduction to the most fundamental aspects of elliptic hypergeometric functions. We will also give some indication of their historical origin in statistical mechanics. We will explain how elliptic hypergeometric functions can be used to construct biorthogonal rational functions, generalizing the famous Askey scheme of orthogonal polynomials. Apart from some general mathematical maturity, the only prerequisites will be elementary linear algebra and complex function theory.
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| 19. |
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| 20. |
- Rosengren, Hjalmar, 1972
(författare)
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Elliptic pfaffians and solvable lattice models
- 2016
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Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - : IOP Publishing. - 1742-5468. ; 2016:8
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
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