Shashank Kanade

Research Interests
I am currently interested in problems involving representation theory of vertex operator algebras, tensor categories and integer partition identities.
Articles
[E]: Expository   [C]: Conference Proceedings
Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities
+ K. Baker, M. C. Russell, C. Sadowski
Coloured \(\mathfrak{sl}_r\) invariants of torus knots and characters of \(\mathcal{W}_r\) algebras
Submitted.
[C] Searching for modular companions
Meh.
On certain identities involving Nahm-type sums with double poles
+ A. Milas and M. C. Russell
Adv. in Appl. Math. (Accepted)
Completing the \(\mathrm{A}_2\) Andrews-Schilling-Warnaar identities
+ M. C. Russell
Int. Math. Res. Not. IMRN (Accepted)
\(A_{2l}^{(2)}\) at level \(-l-\frac{1}{2}\)
J. Algebra (2022)
On \(q\)-series for principal characters of standard \(A_2^{(2)}\)-modules
+ M. C. Russell
Adv. Math. (2022)
Gluing vertex algebras
+ T. Creutzig and R. McRae
Adv. Math. (2022)
Braided Tensor Categories related to \(\mathcal{B}_p\) Vertex Algebras
+ J. Auger, T. Creutzig and M. Rupert
Commun. Math. Phys. (2020)
[C] A variant of IdentityFinder and some new identities of Rogers-Ramanujan-MacMahon type
+ D. Nandi, M. C. Russell
Ann. Comb., Combinatory Analysis 2018: In Honor of George Andrews’ 80th Birthday
[E, C] NGK and HLZ: Fusion for Physicists and Mathematicians
+ D. Ridout
Springer INdAM Series: Affine, Vertex and W-algebras (2020)
Cosets, characters and fusion for admissible-level \(\mathfrak{osp}(1|2)\) minimal models
+ T. Creutzig, T. Liu, D. Ridout
Nucl. Phys. B. (2019)
Universal two-parameter even spin \(\mathcal{W}_\infty\)-algebra
+ A. R. Linshaw
Adv. Math. (2019)
Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type
+ M. C. Russell
Electron. J. Combin. (2019)
Representation theory of \(L_k(\mathfrak{osp}(1|2))\) from vertex tensor categories and Jacobi forms
+ T. Creutzig and J. Frohlich
Proc. Amer. Math. Soc. (2018)
Tensor categories for vertex operator superalgebra extensions
+ T. Creutzig and R. McRae
Mem. Amer. Math. Soc. (Accepted)
Schur-Weyl Duality for Heisenberg cosets
+ T. Creutzig, A. R. Linshaw and D. Ridout
Transf. Groups. (2019)
Simple current extensions beyond semi-simplicity
+ T. Creutzig and A. R. Linshaw
Commun. Contemp. Math. (2020)
On a Koszul complex related to the principal subspace of the basic vacuum module for \(A^{(1)}_1\)
J. Pure and Appl. Alg. (2018)
Structure of certain level \(2\) standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities
Ramanujan J. (2018)
IdentityFinder and some new identities of Rogers-Ramanujan type
+ M. C. Russell
Exp. Math. (2015)
Ghost series and a motivated proof of the Andrews-Bressoud identities
+ J. Lepowsky, M. C. Russell and A. V. Sills
J. Combin. Theory Ser. A. (2017)
A motivated proof of the Göllnitz-Gordon-Andrews identities
+ B. Coulson, J. Lepowsky, R. McRae, F. Qi, M. C. Russell and C. Sadowski
Ramanujan J. (2017)