%0 Generic %1 botta2022framed %A Botta, Tommaso Maria %D 2022 %K Coha %T Framed cohomological Hall algebras and stable envelopes I %U http://arxiv.org/abs/2207.06280 %X There 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 $Y^Q_MO$ 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 $M_Q(v,w)$ for all dimension vectors $v$ and framing vectors $w$ 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.

@misc{botta2022framed, abstract = {There 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 $Y^{Q}_{MO}$ 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 $\mathcal{M}_Q(\text{v},\text{w})$ for all dimension vectors $\text{v}$ and framing vectors $\text{w}$ 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.}, added-at = {2022-07-14T23:19:56.000+0200}, author = {Botta, Tommaso Maria}, biburl = {https://www.bibsonomy.org/bibtex/2711f9d9b9e0afb52abe1511a29717e39/dragosf}, description = {Framed cohomological Hall algebras and stable envelopes I}, interhash = {88bf967ed14b44f3d1185287e0f666e0}, intrahash = {711f9d9b9e0afb52abe1511a29717e39}, keywords = {Coha}, note = {cite arxiv:2207.06280Comment: 34 pages}, timestamp = {2022-07-14T23:19:56.000+0200}, title = {Framed cohomological Hall algebras and stable envelopes I}, url = {http://arxiv.org/abs/2207.06280}, year = 2022 }