Geodesic
Generalized theta series and monodromy of a~Casimir connection. Case of rank~1
Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 201-208

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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.
Mots-clés : Casimir connection monodromy, Verma modules
Keywords: incomplete Appell–Lerch sums. 
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     author = {E. I. Dotsenko},
     title = {Generalized theta series and monodromy of {a~Casimir} connection. {Case} of rank~1},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {201--208},
     publisher = {mathdoc},
     volume = {219},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a0/}
}
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E. I. Dotsenko. Generalized theta series and monodromy of a~Casimir connection. Case of rank~1. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/TMF_2024_219_2_a0/