The Promise Constraint Satisfaction Problem (PCSP) is a generalization of the Constraint Satisfaction Problem (CSP). In a [LICS '19] paper it was shown that a specific PCSP, the problem to find a valid Not-All-Equal solution to a 1-in-3-SAT instance, is not finitely tractable in that it can be solved by a trivial reduction to a tractable CSP, but such a CSP is necessarily over an infinite domain (unless P=NP). We further explore this phenomenon: we give a general necessary condition for finite tractability and characterize finite tractability within a class of templates - the "basic" tractable cases in the dichotomy theorem for symmetric Boolean PCSPs allowing negations by Brakensiek and Guruswami [SODA'18]. This is a joint work with Libor Barto.
Building on the work of Calaque-Enriquez-Etingof, Lyubashenko-Majid, and Arakawa-Suzuki, Jordan constructed a functor from quantum -modules on general linear groups to representations of the double affine Hecke algebra (DAHA) in type . When we input quantum functions on GL(N) the output is , the irreducible DAHA representation indexed by an rectangle. For the specified parameters is Y-semisimple, i.e. one can diagonalize the Dunkl operators. We give an explicit combinatorial description of this module via its Y-weight basis. This is joint work with David Jordan.
The rectangular representation of the double affine Hecke algebra via elliptic Schur-Weyl duality