Generalized theta series and monodromy of a Casimir connection. Case of rank 1

E. I. Dotsenko

National Research Centre "Kurchatov Institute", Moscow, Russia

Abstract: The monodromy of the $\mathfrak{sl}(2)$ Casimir connection is considered. It is shown that the trace of the monodromy operator over an appropriate space of flat sections gives the Jacobi theta constant and incomplete theta functions. A definition of new objects, namely, incomplete Appell–Lerch sums, is given, and their connection with the trace of the monodromy operator is revealed.

Keywords: Casimir connection monodromy, Verma modules, incomplete Appell–Lerch sums.

MSC: 17B10, 81R50

Received: 28.09.2023
Revised: 05.02.2024

DOI: 10.4213/tmf10619

 English version: Theoretical and Mathematical Physics, 2024, 219:2, 705–711

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