Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Orbifolds of symplectic fermion algebras
HTML articles powered by AMS MathViewer

by Thomas Creutzig and Andrew R. Linshaw PDF
Trans. Amer. Math. Soc. 369 (2017), 467-494 Request permission

Abstract:

We present a systematic study of the orbifolds of the rank $n$ symplectic fermion algebra $\mathcal {A}(n)$, which has full automorphism group $Sp(2n)$. First, we show that $\mathcal {A}(n)^{Sp(2n)}$ and $\mathcal {A}(n)^{GL(n)}$ are $\mathcal {W}$-algebras of type $\mathcal {W}(2,4,\dots , 2n)$ and $\mathcal {W}(2,3,\dots , 2n+1)$, respectively. Using these results, we find minimal strong finite generating sets for $\mathcal {A}(mn)^{Sp(2n)}$ and $\mathcal {A}(mn)^{GL(n)}$ for all $m,n\geq 1$. We compute the characters of the irreducible representations of $\mathcal {A}(mn)^{Sp(2n)\times SO(m)}$ and $\mathcal {A}(mn)^{GL(n)\times GL(m)}$ appearing inside $\mathcal {A}(mn)$, and we express these characters using partial theta functions. Finally, we give a complete solution to the Hilbert problem for $\mathcal {A}(n)$; we show that for any reductive group $G$ of automorphisms, $\mathcal {A}(n)^G$ is strongly finitely generated
References
Similar Articles
Additional Information
  • Thomas Creutzig
  • Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
  • MR Author ID: 832147
  • ORCID: 0000-0002-7004-6472
  • Email: creutzig@ualberta.ca
  • Andrew R. Linshaw
  • Affiliation: Department of Mathematics, University of Denver, Denver, Colorado 80208
  • MR Author ID: 791304
  • Email: andrew.linshaw@du.edu
  • Received by editor(s): May 21, 2014
  • Received by editor(s) in revised form: January 8, 2015
  • Published electronically: May 6, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 467-494
  • MSC (2010): Primary 13A50, 17B69; Secondary 11F22, 17B65
  • DOI: https://doi.org/10.1090/tran6664
  • MathSciNet review: 3557781