Elliptic stable envelopes and hypertoric loop spaces

Abstract

Abstract This paper describes a relation between the elliptic stable envelopes of a hypertoric variety

$$X$$

X

and a distinguished K-theory class on the product of the loop hypertoric space

$$\widetilde{\mathscr {L}}X$$

L ~

X

and its symplectic dual

$$\mathscr {P}X^!$$

P

X !

. This class intertwines the K-theoretic stable envelopes in a certain limit. Our results are suggestive of a possible categorification of elliptic stable envelopes.