scholarly journals BRAID GROUP ACTIONS FROM CATEGORICAL SYMMETRIC HOWE DUALITY ON DEFORMED WEBSTER ALGEBRAS

2021 ◽  
Author(s):  
M. KHOVANOV ◽  
A. D. LAUDA ◽  
J. SUSSAN ◽  
Y. YONEZAWA
Keyword(s):  
Braid Group ◽  
Group Actions ◽  
Howe Duality

Stability conditions and braid group actions on affine An quivers

2021 ◽  
pp. 2250174
Author(s):  
Chien-Hsun Wang
Keyword(s):  
Moduli Space ◽  
Braid Group ◽  
Group Actions ◽  
Stability Conditions ◽  
Quadratic Differentials ◽  
Spherical Subgroup ◽  
Type Formula ◽  
Affine Type

We study stability conditions on the Calabi–Yau-[Formula: see text] categories associated to an affine type [Formula: see text] quiver which can be constructed from certain meromorphic quadratic differentials with zeroes of order [Formula: see text]. We follow Ikeda’s work to show that this moduli space of quadratic differentials is isomorphic to the space of stability conditions quotient by the spherical subgroup of the autoequivalence group. We show that the spherical subgroup is isomorphic to the braid group of affine type [Formula: see text] based on the Khovanov–Seidel–Thomas method.

scholarly journals Braid group actions via categorified Heisenberg complexes

2013 ◽  
Vol 150 (1) ◽  
pp. 105-142 ◽  
Author(s):  
Sabin Cautis ◽  
Anthony Licata ◽  
Joshua Sussan
Keyword(s):  
Braid Group ◽  
Group Actions ◽  
Heisenberg Algebra ◽  
Vertex Operators

AbstractWe construct categorical braid group actions from 2-representations of a Heisenberg algebra. These actions are induced by certain complexes which generalize spherical (Seidel–Thomas) twists and are reminiscent of the Rickard complexes defined by Chuang–Rouquier. Conjecturally, one can relate our complexes to Rickard complexes using categorical vertex operators.

Analogues of quantum Schubert cell algebras in PBW-deformations of quantum groups

2016 ◽  
Vol 15 (10) ◽  
pp. 1650179 ◽  
Author(s):  
Yongjun Xu ◽  
Dingguo Wang ◽  
Jialei Chen
Keyword(s):  
Weyl Group ◽  
Quantum Groups ◽  
Braid Group ◽  
Group Actions ◽  
Necessary Condition ◽  
Quantum Algebras ◽  
Ore Extension ◽  
Schubert Cell ◽  
Sufficient And Necessary Condition

We focus on a class of filtered quantum algebras [Formula: see text] which are both coideal subalgebras of quantum groups and Poincaré–Birkhoff–Witt (PBW)-deformations of their negative parts. In [Y. Xu and S. Yang, PBW-deformations of quantum groups, J. Algebra 408 (2014) 222–249], Xu and Yang proved that braid group actions on [Formula: see text] introduced by Kolb and Pellegrini can be used to define root vectors and construct PBW bases for [Formula: see text]. In this present paper, for each element [Formula: see text] in the Weyl group of [Formula: see text] we first introduce a subspace [Formula: see text] and a subalgebra [Formula: see text] of [Formula: see text], where [Formula: see text] can be considered as an analogue of quantum Schubert cell algebra. Then a sufficient and necessary condition on [Formula: see text] is given for [Formula: see text]. Moreover, we prove that [Formula: see text] if and only if [Formula: see text] and [Formula: see text] can be generated by the same simple reflections. Finally, we characterize the algebra [Formula: see text] which can be obtained via an iterated Ore extension. Our results show that quantum groups and their PBW-deformations really have some different properties.

scholarly journals Quivers, Floer cohomology, and braid group actions

2001 ◽  
Vol 15 (1) ◽  
pp. 203-271 ◽  
Author(s):  
Mikhail Khovanov ◽  
Paul Seidel
Keyword(s):  
Braid Group ◽  
Group Actions ◽  
Floer Cohomology

Finite Hurwitz braid group actions for Artin groups

2004 ◽  
Vol 143 (1) ◽  
pp. 189-222 ◽  
Author(s):  
Stephen P. Humphries
Keyword(s):  
Braid Group ◽  
Group Actions ◽  
Artin Groups

scholarly journals Braiding via geometric Lie algebra actions

2012 ◽  
Vol 148 (2) ◽  
pp. 464-506 ◽  
Author(s):  
Sabin Cautis ◽  
Joel Kamnitzer
Keyword(s):  
Lie Algebra ◽  
Braid Group ◽  
Group Actions ◽  
Derived Categories ◽  
Flag Varieties ◽  
Coherent Sheaves ◽  
Cotangent Bundles ◽  
Partial Flag Varieties

AbstractWe introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra. The same proof shows that strong categorical actions in the sense of Khovanov–Lauda and Rouquier also lead to braid group actions. As an example, we construct an action of Artin’s braid group on derived categories of coherent sheaves on cotangent bundles to partial flag varieties.

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