On cohomological Hall algebras of quivers: Generators
On cohomological Hall algebras of quivers: Generators
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关于箭袋的上同调霍尔代数：生成器
DOI：
10.1515/crelle-2018-0004
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
E. Vasserot
中科院分区：
文献类型：
--
作者：
O. Schiffmann;E. Vasserot
Abstract We study the cohomological Hall algebra Y♭{\operatorname{Y}\nolimits^{\flat}} of a Lagrangian substack Λ♭{\Lambda^{\flat}} of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and their actions on the cohomology of Nakajima quiver varieties. We prove that Y♭{\operatorname{Y}\nolimits^{\flat}} is pure and we compute its Poincaré polynomials in terms of (nilpotent) Kac polynomials. We also provide a family of algebra generators. We conjecture that Y♭{\operatorname{Y}\nolimits^{\flat}} is equal, after a suitable extension of scalars, to the Yangian ?{\mathbb{Y}} introduced by Maulik and Okounkov. As a corollary, we prove a variant of Okounkov’s conjecture, which is a generalization of the Kac conjecture relating the constant term of Kac polynomials to root multiplicities of Kac–Moody algebras.
Abstract We study the cohomological Hall algebra Y♭{\operatorname{Y}\nolimits^{\flat}} of a Lagrangian substack Λ♭{\Lambda^{\flat}} of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and their actions on the cohomology of Nakajima quiver varieties. We prove that Y♭{\operatorname{Y}\nolimits^{\flat}} is pure and we compute its Poincaré polynomials in terms of (nilpotent) Kac polynomials. We also provide a family of algebra generators. We conjecture that Y♭{\operatorname{Y}\nolimits^{\flat}} is equal, after a suitable extension of scalars, to the Yangian ?{\mathbb{Y}} introduced by Maulik and Okounkov. As a corollary, we prove a variant of Okounkov’s conjecture, which is a generalization of the Kac conjecture relating the constant term of Kac polynomials to root multiplicities of Kac–Moody algebras.
对称性、可积性和几何：方法和应用箭袋品种和分支⋆
影响因子：
1.8
作者：
L. Florentin;Chrysanthy Bili;K. Kekou;N. Tripodis;A. Mavrou;C. Metaxotou
通讯作者：
C. Metaxotou
影响因子：
3.9
作者：
H. Nakajima
通讯作者：
H. Nakajima