scholarly journals $$ \mathfrak{gl} $$N Higgsed networks

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Yegor Zenkevich
Keyword(s):  
Lie Algebra ◽  
Partition Functions ◽  
Toroidal Algebra

Abstract We generalize the framework of Higgsed networks of intertwiners to the quantum toroidal algebra associated to Lie algebra $$ \mathfrak{gl} $$ gl N. Using our formalism we obtain a systems of screening operators corresponding to W-algebras associated to toric strip geometries and reproduce partition functions of 3d theories on orbifolded backgrounds.

scholarly journals (q, t)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
Hidetoshi Awata ◽  
Hiroaki Kanno ◽  
Andrei Mironov ◽  
Alexei Morozov ◽  
Kazuma Suetake ◽  
...  
Keyword(s):  
Partition Functions ◽  
Toroidal Algebra ◽  
Nekrasov Partition Functions

scholarly journals Multipartitions, generalized Durfee squares and affine Lie algebra characters

2002 ◽  
Vol 72 (3) ◽  
pp. 395-408 ◽  
Author(s):  
Peter Bouwknegt
Keyword(s):  
Lie Algebra ◽  
Partition Functions ◽  
Affine Lie Algebra ◽  
Higher Dimensional ◽  
Durfee Square ◽  
Durfee Squares

AbstractWe give some higher dimensional analogues of the Durfee square formula and point out their relation to dissections of multipartitions. We apply the results to write certain affine Lie algebra characters in terms of Universal Chiral Partition Functions.

Automorphism Group of a Class of Gradation Shifting Toroidal Lie Algebras

2010 ◽  
Vol 17 (04) ◽  
pp. 705-720 ◽  
Author(s):  
Zhangsheng Xia ◽  
Shaobin Tan ◽  
Haifeng Lian
Keyword(s):  
Automorphism Group ◽  
Vector Space ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Linear Groups ◽  
Type B ◽  
Laurent Polynomials ◽  
Lie Bracket ◽  
Toroidal Algebra ◽  
Toroidal Lie Algebra

Let [Formula: see text] be the ring of Laurent polynomials in commuting variables. As a generalization of the toroidal Lie algebra, the gradation shifting toroidal Lie algebra [Formula: see text] is isomorphic to the corresponding (centerless) toroidal Lie algebra so(n, ℂ) ⨂ A of type B or D as a vector space, with the Lie bracket twisted by n fixed elements E1,…,En from A. In this paper, we study the automorphisms of the gradation shifting toroidal algebra [Formula: see text], which is proved to be closely related to a class of subgroups of GL(n,ℤ), called the linear groups over semilattices. We use the linear group over a special semilattice to determine the automorphism group of the gradation shifting toroidal algebra [Formula: see text], which extends our earlier work.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

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