scholarly journals Quiver varieties and Hall algebras

2016 ◽  
Vol 112 (6) ◽  
pp. 1002-1018 ◽  
Author(s):  
Sarah Scherotzke ◽  
Nicolo Sibilla
Keyword(s):  
Quiver Varieties ◽  
Hall Algebras

scholarly journals On cohomological Hall algebras of quivers: Generators

2020 ◽  
Vol 2020 (760) ◽  
pp. 59-132 ◽  
Author(s):  
Olivier Schiffmann ◽  
Eric Vasserot
Keyword(s):  
Constant Term ◽  
Hall Algebra ◽  
Preprojective Algebra ◽  
Quiver Varieties ◽  
Hall Algebras ◽  
Root Multiplicities ◽  
Moduli Stack

AbstractWe study the cohomological Hall algebra {\operatorname{Y}\nolimits^{\flat}} of a Lagrangian substack {\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 {\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 {\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.

scholarly journals Hall algebras and quantum symmetric pairs III: Quiver varieties

2021 ◽  
Vol 393 ◽  
pp. 108071
Author(s):  
Ming Lu ◽  
Weiqiang Wang
Keyword(s):  
Quiver Varieties ◽  
Hall Algebras

scholarly journals An introduction to motivic Hall algebras

2012 ◽  
Vol 229 (1) ◽  
pp. 102-138 ◽  
Author(s):  
Tom Bridgeland
Keyword(s):  
Hall Algebras

scholarly journals Hall algebras and quantum Frobenius

2010 ◽  
Vol 154 (1) ◽  
pp. 181-206 ◽  
Author(s):  
Kevin Mcgerty
Keyword(s):  
Hall Algebras

scholarly journals Semistable Chow–Hall algebras of quivers and quantized Donaldson–Thomas invariants

2018 ◽  
Vol 12 (5) ◽  
pp. 1001-1025 ◽  
Author(s):  
Hans Franzen ◽  
Markus Reineke
Keyword(s):  
Hall Algebras

scholarly journals Quantum groups via cyclic quiver varieties I

2015 ◽  
Vol 152 (2) ◽  
pp. 299-326 ◽  
Author(s):  
Fan Qin
Keyword(s):  
Quantum Groups ◽  
Bilinear Form ◽  
Canonical Basis ◽  
Natural Basis ◽  
Grothendieck Ring ◽  
Quiver Varieties ◽  
Enveloping Algebra ◽  
Dual Canonical Basis ◽  
Quantized Enveloping Algebra ◽  
Cyclic Quiver

We construct the quantized enveloping algebra of any simple Lie algebra of type $\mathbb{A}\mathbb{D}\mathbb{E}$ as the quotient of a Grothendieck ring arising from certain cyclic quiver varieties. In particular, the dual canonical basis of a one-half quantum group with respect to Lusztig’s bilinear form is contained in the natural basis of the Grothendieck ring up to rescaling. This paper expands the categorification established by Hernandez and Leclerc to the whole quantum groups. It can be viewed as a geometric counterpart of Bridgeland’s recent work for type $\mathbb{A}\mathbb{D}\mathbb{E}$.

scholarly journals On the number of points of nilpotent quiver varieties over finite fields

2020 ◽  
Vol 53 (6) ◽  
pp. 1501-1544
Author(s):  
Tristan BOZEC ◽  
Olivier SCHIFFMANN ◽  
Eric VASSEROT
Keyword(s):  
Finite Fields ◽  
Quiver Varieties
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