An Introduction to Birational Weyl Group Actions

2002 ◽  
pp. 179-222 ◽  
Author(s):  
Masatoshi Noumi
Keyword(s):  
Weyl Group ◽  
Group Actions

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 N-soliton solutions to the DKP equation and Weyl group actions

2006 ◽  
Vol 39 (15) ◽  
pp. 4063-4086 ◽  
Author(s):  
Yuji Kodama ◽  
Ken-Ichi Maruno
Keyword(s):  
Weyl Group ◽  
Group Actions ◽  
Soliton Solutions ◽  
Dkp Equation

scholarly journals Quiver varieties and Weyl group actions

2000 ◽  
Vol 50 (2) ◽  
pp. 461-489 ◽  
Author(s):  
George Lusztig
Keyword(s):  
Weyl Group ◽  
Group Actions ◽  
Quiver Varieties

QUASI-SPLIT SYMMETRIC PAIRS OF AND THEIR SCHUR ALGEBRAS

2020 ◽  
pp. 1-27
Author(s):  
YIQIANG LI ◽  
JIERU ZHU
Keyword(s):  
Weyl Group ◽  
Group Actions ◽  
Type B ◽  
Schur Algebras

Abstract We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in [1] specialized at $q=1$ .

Weyl group actions

2013 ◽  
pp. 42-69
Author(s):  
R. M. Green
Keyword(s):  
Weyl Group ◽  
Group Actions

scholarly journals Weyl group actions on the Springer sheaf

2013 ◽  
Vol 108 (6) ◽  
pp. 1501-1528 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Daniel Juteau ◽  
Simon Riche
Keyword(s):  
Weyl Group ◽  
Group Actions

scholarly journals A comparison of Weyl group actions on Lagrangian cycles

1998 ◽  
Vol 9 (2) ◽  
pp. 173-181
Author(s):  
Mladen Boz̆ic̆ević
Keyword(s):  
Weyl Group ◽  
Group Actions
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