Invariants of Superalgebras as Complex Integrals

2025/11/24 by Berele, Allan
Mathematics · #16R30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2511.19361

openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

In [A. Berele, Computing super matrix invariants, \it Advances in Applied Math. \bf48 (2012), 273--289.] we defined integrals that approximated the Poincaré 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 Poincaré series. The purpose of this paper is to prove that Budzik's ideas are correct. As a consequence we prove that the Poincaré series are rational functions.

Citations

• Supergroup Invariants and the Brane/Negative Brane Expansion
• Computing Super Matrix Invariants
• Some remarks on the characters of the general Lie superalgebra
• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes

Related

• Computing Super Matrix Invariants
• On Fundamental Theorems of Invariant Theory for the Special Linear Supergroup
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• Integration on Lie supergroups. A Hopf superalgebra approach
• An analog of the classical invariant theory for Lie superlagebras. II