Orbifolds of symplectic fermion algebras

Creutzig T, Linshaw AR (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Transactions of the American Mathematical Society American Mathematical Society

Book Volume: 369

Pages Range: 467-494

Journal Issue: 1

DOI: 10.1090/tran6664

Abstract

We present a systematic study of the orbifolds of the rank n symplectic fermion algebra A(n), which has full automorphism group Sp(2n). First, we show that A(n)^Sp(2n) and A(n)GL⁽ⁿ⁾ are W-algebras of type W(2, 4,…, 2n) and W(2, 3,…, 2n + 1), respectively. Using these results, we find minimal strong finite generating sets for A(mn)^Sp(2n) and A(mn)^GL(n) for all m, n ≥ 1. We compute the characters of the irreducible representations of A(mn)^Sp(2n)^ï¿½^SO(m) and A(mn)^GL(n)^ï¿½^GL(m) appearing inside A(mn), and we express these characters using partial theta functions. Finally, we give a complete solution to the Hilbert problem for A(n); we show that for any reductive group G of automorphisms, A(n)^G is strongly finitely generated.

Involved external institutions

University of Alberta

Canada (CA) University of Denver

United States (USA) (US)

How to cite

APA:

Creutzig, T., & Linshaw, A.R. (2017). Orbifolds of symplectic fermion algebras. Transactions of the American Mathematical Society, 369(1), 467-494. https://doi.org/10.1090/tran6664

MLA:

Creutzig, Thomas, and Andrew R. Linshaw. "Orbifolds of symplectic fermion algebras." Transactions of the American Mathematical Society 369.1 (2017): 467-494.

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