ON SOME VERTEX ALGEBRAS RELATED TO $$ {V}_{-1}\left(\mathfrak{sl}(n)\right) $$ AND THEIR CHARACTERS

Abstract

We investigate vertex operator algebras L(k, 0) associated with modular-invariant representations for an affine Lie algebra A(1) 1 , where k is 'admissible' rational number. We show that VOA L(k, 0) is rational in the category O and find all irreducible representations in the category of weight modules.

Generalized multiple q-zeta values and characters of vertex algebras

“…It was observed in [11] that non-isomorphic graphs can have identical graph series. For example, the 5-cycle C 5 (later also denoted by Γ 5 ) and E 6 graphs: 1 Another "standard" form is (1 − q) a 1 +•••+a k ζq(a 1 , ..., a k ) [15] give the same graph series up to an Euler factor :…”

“…In an unrelated work [1], Adamović and the author constructed another family of vertex (super)algebras U (m) , m ≥ 3. They are expected to share properties with those in the S-class [13,9] and Deligne's series [5] including quasi-modularity of characters.…”

“…Characters and supercharacters of the U family of vertex algebras. Adamović and the author introduced in [1] a new family of vertex (super)algebras somewhat related to those in the S-class and Deligne's series [5,9]. We will refer to them as the U family of vertex algebras and denote them by U (m) .…”

“…For m odd, U (m) is a Z-graded vertex superalgebra, so it important to consider its supercharacter sch[U (m) ](τ ). For m even, U (m) is a vertex algebra with 1 2 Z ≥0 -grading. We only consider m is odd case here for simplicity.…”

“…where s := m − 2ℓ − 1 ≥ 0 is even. For s = 0, this sum equals 1 24 (1 − E 2 (τ )) ∈ QM. For s ≥ 2, the sum is the first (q d dq )-derivative of the Eisenstein series E s−1 (τ ) and thus in QM.…”