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arXiv · 2511.19361

Invariants of Superalgebras as Complex Integrals

Allan Berele
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Abstract

In [A. Berele, Computing super matrix invariants, {\it Advances in Applied Math. \bf48} (2012), 273--289.] we defined integrals that approximated the Poincar\'e series of the invariants and concomitants of the general linear Lie supergroup or superalgebra. Budzik suggested in [K. Budzik, Supergroup Invariants and the Brane/Negative Brane Expansion, (preprint) arXiv:2509.20451] a way to adapt this method to get the exact Poincar\'e series. The purpose of this paper is to prove that Budzik's ideas are correct. As a consequence we prove that the Poincar\'e series are rational functions.

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Allan Berele. 2025-11-24. Invariants of Superalgebras as Complex Integrals. https://arxiv.org/abs/2511.19361

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