Elliptic determinant evaluations and the Macdonald identities for affine root systems

By Hjalmar Rosengren, Michael J. Schlosser. Compositio Mathematica, 2005

65 citations recorded by the source corpus.

We obtain several determinant evaluations, related to affine root systems, which provide elliptic extensions of Weyl denominator formulas. Some of these are new, also in the polynomial special case, while others yield new proofs of the Macdonald identities for the seven infinite families of irreducible reduced affine root systems.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fc34941423f670e20a87666915ccedc82821f908

How researchers see this paper

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In Discrete Mathematics and Combinatorics

1. V. Spiridonov
2. Michael J. Schlosser
3. S. Ole Warnaar
4. Hjalmar Rosengren

In Geometry and Topology

1. V. Spiridonov
2. Michael J. Schlosser
3. G. Vartanov
4. Abhijit Gadde
5. Y. Imamura

In Mathematical Physics

1. V. Spiridonov
2. Michael J. Schlosser

Citations in the corpus

• Essays on the theory of elliptic hypergeometric functions (2008, background): “In the paper [92], Rosengren and Schlosser have systematically considered determinants of theta functions on root systems (in particular, this paper contains a detailed list of references on this subject) and constructed a number of new exactly computable cases, which we skip for brevity.”
• Multilateral Inversion of Ar, Cr, and Dr Basic Hypergeometric Series (2006, background): “7) are closely associated with the product side of the Weyl denominator formulae for the respective root systems, see [4, 22, 28].”