S. Kanade

activity

20142026

most citedTensor categories for vertex operator superalgebra extensions

92 citations · 389 across the 26 of their papers we have counts for

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11 papers · 1 filter

math.QA2026

Classical freeness of $sl_{n}$ at level $1$ via combinatorics

Shashank Kanade

We use a family of Rogers--Ramanujan-type combinatorial identities of Dousse--Konan involving coloured partitions to prove classical freeness of the simple vertex operator algebras…

math.QA2024

Coloured invariants of torus knots, $W$ algebras, and relative asymptotic weight multiplicities

Shashank Kanade

We study coloured invariants of torus knots $T (p, p^{'})$ (where $p, p^{'}$ are coprime positive integers). When the colouring Lie algebra is simply-laced, and when $p, p^{'} \geq h^{\lor}$ , we u…

math.QA2023

Characters of logarithmic vertex operator algebras and coloured invariants of torus links

Shashank Kanade

We show that the characters of $sl_{r}$ versions of the $(1, p)$ singlet and the $(1, p)$ triplet VOAs arise as limits of appropriately coloured $sl_{r}$ Jones inva…

math.QA2022★ 3 cited

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

Shashank Kanade

Let $p < p^{'}$ be a pair of coprime positive integers. In this note, generalizing Morton's work in the case of $sl_{2}$ , we give a formula for the $sl_{r}$ Jones inva…

math.QA2020

$A_{2 l}^{(2)}$ at level $- l - \frac{1}{2}$

Shashank Kanade

Let $L_{l} = L (sl_{2 l + 1}, - l - \frac{1}{2})$ be the simple vertex operator algebra based on the affine Lie algebra $sl_{2 l + 1}$ at boundary admissible lev…

math.QA2019★ 26 cited

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

Jean Auger, Thomas Creutzig, Shashank Kanade +1

The $B_{p}$ -algebras are a family of vertex operator algebras parameterized by $p \in Z_{\geq 2}$ . They are important examples of logarithmic CFTs and appear as chir…

math.QA2019★ 31 cited

Gluing vertex algebras

Thomas Creutzig, Shashank Kanade, Robert McRae

We relate commutative algebras in braided tensor categories to braid-reversed tensor equivalences, motivated by vertex algebra representation theory. First, for $C$ a bra…

math.QA2017★ 5 cited

Representation theory of $L_{k} (osp (1∣2))$ from vertex tensor categories and Jacobi forms

Thomas Creutzig, Jesse Frohlich, Shashank Kanade

The purpose of this work is to illustrate in a family of interesting examples how to study the representation theory of vertex operator superalgebras by combining the theory of ver…

math.QA2017★ 92 cited

Tensor categories for vertex operator superalgebra extensions

Thomas Creutzig, Shashank Kanade, Robert McRae

Let $V$ be a vertex operator algebra with a category $C$ of (generalized) modules that has vertex tensor category structure, and thus braided tensor category structure, a…

math.QA2016★ 86 cited

Schur-Weyl Duality for Heisenberg Cosets

Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw +1

Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C = Com (H, V)$ be the coset of $H$ in $V$ . Assumin…

math.QA2015★ 65 cited

Simple current extensions beyond semi-simplicity

Thomas Creutzig, Shashank Kanade, Andrew R. Linshaw

Let V be a simple VOA and consider a representation category of V that is a vertex tensor category in the sense of Huang-Lepowsky. In particular, this category is a braided tensor…

Classical freeness of sln​ at level 1 via combinatorics

Coloured invariants of torus knots, W algebras, and relative asymptotic weight multiplicities

Characters of logarithmic vertex operator algebras and coloured invariants of torus links

Coloured slr​ invariants of torus knots and characters of Wr​ algebras

A2l(2)​ at level −l−21​

Braided Tensor Categories related to Bp​ Vertex Algebras

Gluing vertex algebras

Representation theory of Lk​(osp(1∣2)) from vertex tensor categories and Jacobi forms

Tensor categories for vertex operator superalgebra extensions

Schur-Weyl Duality for Heisenberg Cosets

Simple current extensions beyond semi-simplicity

Classical freeness of $sl_{n}$ at level $1$ via combinatorics

Coloured invariants of torus knots, $W$ algebras, and relative asymptotic weight multiplicities

Coloured $sl_{r}$ invariants of torus knots and characters of $W_{r}$ algebras

$A_{2 l}^{(2)}$ at level $- l - \frac{1}{2}$

Braided Tensor Categories related to $B_{p}$ Vertex Algebras

Representation theory of $L_{k} (osp (1∣2))$ from vertex tensor categories and Jacobi forms