Rogers–Ramanujan identities via Nil-DAHA

Almost by design, Nil-DAHA provides Dunkl operators and other tools (algebraic and analytic) in the Q-Toda theory. As Boris Feigin and the speaker demonstrated recently, Nil-DAHA has important connections with the coset algebras and can be used to build the theory of Rogers–Ramanujan identities of modular type associated with root systems. The Rogers–Ramanujan sums we obtain quantize the constant Y-systems (of type $RxA_n$ for any reduced root systems $R$). This involves physics, dilogarithm identities and a lot of interesting arithmetic, though the talk will be mainly focused on the core construction.