The Virasoro fusion kernel and Ruijsenaars’ hypergeometric function. (English) Zbl 1456.81400
Summary: We show that the Virasoro fusion kernel is equal to Ruijsenaars’ hypergeometric function up to normalization. More precisely, we prove that the Virasoro fusion kernel is a joint eigenfunction of four difference operators. We find a renormalized version of this kernel for which the four difference operators are mapped to four versions of the quantum relativistic hyperbolic Calogero-Moser Hamiltonian tied with the root system \(BC_1\). We consequently prove that the renormalized Virasoro fusion kernel and the corresponding quantum eigenfunction, the (renormalized) Ruijsenaars hypergeometric function, are equal.
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81Q80 | Special quantum systems, such as solvable systems |
| 17B60 | Lie (super)algebras associated with other structures (associative, Jordan, etc.) |
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
| 17B22 | Root systems |
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