2023/08/14 by Botta, Tommaso Maria, Rimanyi, Richard · 1 citation
#14C17 #14J33 #20G42 #55N34 #81T30 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2308.07300
In this paper we study the elliptic characteristic classes known as ''stable envelopes'', which were introduced by M. Aganagic and A. Okounkov. We prove that for a rich class of holomorphic symplectic varieties\unicodex2013called Cherkis bow varieties\unicodex2013their elliptic stable envelopes exhibit a duality property inspired by mirror symmetry in d=3, \mathcal N=4 quantum field theories. A crucial step of our proof involves the process of ''resolving'' large charge branes into multiple smaller charge branes. This phenomenon turns out to be the geometric counterpart of the algebraic fusion procedure. Along the way we discover various new features in the geometry of bow varieties.