On units in loop algebra $$F[M(Dih(C_p^2),2)]$$ F [ M ( D i h ( C p 2 ) , 2 ) ]

2017 ◽  
Vol 58 (4) ◽  
pp. 765-774
Author(s):  
Swati Sidana
Keyword(s):  
Loop Algebra

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

Automorphism group and representation of a twisted multi-loop algebra

2010 ◽  
Vol 26 (1) ◽  
pp. 143-154 ◽  
Author(s):  
Cui Chen ◽  
Hai Feng Lian ◽  
Shao Bin Tan
Keyword(s):  
Automorphism Group ◽  
Loop Algebra

Loop algebra and visaoro symmetries of integrable hierarchies of KP type

2001 ◽  
Vol 78 (3-4) ◽  
pp. 233-253 ◽  
Author(s):  
H. Aratyn ◽  
J.F. Gomes ◽  
E. Nissimov ◽  
S. Pacheva
Keyword(s):  
Integrable Hierarchies ◽  
Loop Algebra

scholarly journals Asymptotic representations and Drinfeld rational fractions

2012 ◽  
Vol 148 (5) ◽  
pp. 1593-1623 ◽  
Author(s):  
David Hernandez ◽  
Michio Jimbo
Keyword(s):  
Rational Functions ◽  
Loop Algebra ◽  
Explicit Formulas ◽  
Simple Modules ◽  
Asymptotic Representations

AbstractWe introduce and study a category of representations of the Borel algebra associated with a quantum loop algebra of non-twisted type. We construct fundamental representations for this category as a limit of the Kirillov–Reshetikhin modules over the quantum loop algebra and establish explicit formulas for their characters. We prove that general simple modules in this category are classified by n-tuples of rational functions in one variable which are regular and non-zero at the origin but may have a zero or a pole at infinity.

A type of loop algebra and the associated loop algebras

2008 ◽  
Vol 37 (2) ◽  
pp. 552-565 ◽  
Author(s):  
Honwah Tam ◽  
Yufeng Zhang
Keyword(s):  
Loop Algebra ◽  
Loop Algebras

scholarly journals The Semidirect Sum of Lie Algebras and Its Applications to C-KdV Hierarchy

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xia Dong ◽  
Tiecheng Xia ◽  
Desheng Li
Keyword(s):  
Quadratic Form ◽  
Lie Algebras ◽  
Integrable Systems ◽  
The Other ◽  
Loop Algebra ◽  
Hamiltonian Structures ◽  
Kdv Hierarchy ◽  
Integrable Coupling

By use of the loop algebraG-~, integrable coupling of C-KdV hierarchy and its bi-Hamiltonian structures are obtained by Tu scheme and the quadratic-form identity. The method can be used to produce the integrable coupling and its Hamiltonian structures to the other integrable systems.

scholarly journals A Quantization Procedure of Fields Based on Geometric Langlands Correspondence

2009 ◽  
Vol 2009 ◽  
pp. 1-14
Author(s):  
Do Ngoc Diep
Keyword(s):  
Symmetry Group ◽  
Lie Algebra ◽  
Vector Bundles ◽  
Sigma Model ◽  
Fock Space ◽  
Loop Algebra ◽  
Target Space ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
Geometric Langlands

We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing the possible symmetry groupGL. Use the sigma model and momentum maps, we reduce the problem to a problem of quantization of trivial vector bundles with connection over the space dual to the Lie algebra of the symmetry groupGL. After that we quantize the vector bundles with connection over the coadjoint orbits of the symmetry groupGL. Use the electric-magnetic duality to pass to the Langlands dual Lie groupG. Therefore, we have some affine Kac-Moody loop algebra of meromorphic functions with values in Lie algebra=Lie(G). Use the construction of Fock space reprsentations to have representations of such affine loop algebra. And finally, we have the automorphic representations of the corresponding Langlands-dual Lie groupsG.

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