New Partition Identities From Cℓ(1)C_{\ell}^{(1)}-Modules

In this paper we conjecture combinatorial Rogers-Ramanujan type colored partition identities related to standard representations of the affine Lie algebra of type $C^{(1)}_\ell$, $\ell\geq2$, and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras.Comment: 19 page

New partition identities from (C^{(1)}_ell)-modules

In this paper we conjecture combinatorial Rogers-Ramanu­jan type colored partition identities related to standard representations of the affine Lie algebra of type (C^{(1)}_ell), (ellgeq2), and we conjecture similar colored partition identities with no obvious connection to representation theory of affine Lie algebras

The center of small quantum groups II: singular blocks

We generalize to the case of singular blocks the result in Bezrukavnikov and Lachowska [Quantum groups, Contemporary Mathematics 433 (American Mathematical Society, Providence, RI, 2007) 89–101] that describes the center of the principal block of a small quantum group in terms of sheaf cohomology over the Springer resolution. Then using the method developed in Lachowska and Qi [Int. Math. Res. Not., Preprint, 2017, arXiv:1604.07380], we present a linear algebro‐geometric approach to compute the dimensions of the singular blocks and of the entire center of the small quantum group associated with a complex semisimple Lie algebra. A conjectural formula for the dimension of the center of the small quantum group at an l th root of unity is formulated in type A