Abstract
AbstractThere are multiple conjectures relating the cohomological Hall algebras (CoHAs) of certain substacks of the moduli stack of representations of a quiver Q to the Yangian $$Y^{Q}_\textrm{MO}$$
Y
MO
Q
by Maulik–Okounkov, whose construction is based on the notion of stable envelopes of Nakajima varieties. In this article, we introduce the cohomological Hall algebra of the moduli stack of framed representations of a quiver Q (framed CoHA), and we show that the equivariant cohomology of the disjoint union of the Nakajima varieties $${\mathcal {M}}_Q(\text {v},\text {w})$$
M
Q
(
v
,
w
)
for all dimension vectors $$\text {v}$$
v
and framing vectors $$\text {w}$$
w
has a canonical structure of subalgebra of the framed CoHA. Restricted to this subalgebra, the algebra multiplication is identified with the stable envelope map. As a corollary, we deduce an explicit inductive formula to compute stable envelopes in terms of tautological classes.
Funder
National Centres of Competence in Research SwissMAP
Swiss National Science Foundation
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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