A categorical approach to classical and quantum Schur-Weyl duality

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras exemplified by the sequence of group algebras of the symmetric groups and use them to introduce associated monoidal categories. Universal properties of these categories lead to uniform constructions of the Drinfeld functor connecting representation theories of the degenerate affine Hecke algebras and the Yangians and of its q-analogue. Moreover, we construct actions of these categories on certain (infinitesimal) braided categories containing a Hecke object.

💡 Research Summary

The paper presents a unified categorical framework for classical and quantum Schur‑Weyl dualities by introducing the notion of a multiplicative sequence of algebras. A multiplicative sequence consists of algebras (A_n) together with bilinear maps (\mu_{n,m}:A_n\otimes A_m\to A_{n+m}) satisfying associativity and unit conditions. The prototypical example is the family of group algebras (\mathbb{C}