Naslov
On some vertex algebras related to $V_{;;;; -1};;;; (sl(n)) $ and their characters
(On some vertex algebras related to $V_{;;;; -1};;;; (sl(n))$ and their characters)

Autori
Adamović, Dražen ; Milas, Antun

Izvornik
Transformation groups (1083-4362) 26 (2021), 1; 1-30

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
vertex algebras ; affine Lie algebras ; parafermion algebra ; charactersi

Sažetak
We consider several vertex operator algebras and superalgebras closely related to V−1(sl(n)), n ≥ 3 : (a) the parafermionic subalgebra K(sl(n) ; −1) for which we completely describe its inner structure, (b) the vacuum algebra Ω(V−1(sl(n))), and (c) an infinite extension U of V−1(sl(n)) obtained from certain irreducible ordinary modules with integral conformal weights. It turns out that U is isomorphic to the coset vertex algebra psl(n|n)1/sl(n)1, n ≥ 3. We show that V−1(sl(n)) admits precisely n ordinary irreducible modules, up to isomorphism. This leads to the conjecture that U is quasi-lisse.We present evidence in support of this conjecture: we prove that the (super)character of U is quasimodular of weight one by virtue of being the constant term of a meromorphic Jacobi form of index zero. Explicit formulas and MLDE for characters and supercharacters are given for g = sl(3) and outlined for general n. We present a conjectural family of 2nd order MLDEs for characters of vertex algebras psl(n|n)1, n ≥ 2. We finish with a theorem pertaining to characters of psl(n|n)1 and U-modules.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
University at Albany, SAD

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