2025/10/27 by Konno, Hitoshi, Smirnov, Andrey
#14N10 #17B37 #81R10 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2510.22992
We propose a new construction of vertex operators of the elliptic quantum toroidal algebra Ut1,t2,p(\mathfrakglN,tor) by combining representations of the algebra and formulas of the elliptic stable envelopes for the A(1)N-1 quiver variety \cal M(v,w). Compositions of the vertex operators turn out consistent to the shuffle product formula of the elliptic stable envelopes. Their highest to highest expectation values provide K-theoretic vertex functions for \cal M(v,w). We also derive exchange relation of the vertex operators and construct a L-operator satisfying the RLL=LLR^* relation with R and R^* being elliptic dynamical R-matrices defined as transition matrices of the elliptic stable envelopes. Assuming a universal form of L and defining a comultiplication Δ in terms of it, we show that our vertex operators are intertwining operators of the Ut1,t2,p(\mathfrakglN,tor)-modules w.r.t Δ.