scholarly journals Langlands Duality for Finite-Dimensional Representations of Quantum Affine Algebras

2010 ◽  
Vol 96 (1-3) ◽  
pp. 217-261 ◽  
Author(s):  
Edward Frenkel ◽  
David Hernandez
Keyword(s):  
Quantum Affine Algebras ◽  
Langlands Duality ◽  
Finite Dimensional ◽  
Affine Algebras

scholarly journals Finite-dimensional crystals B2,s for quantum affine algebras of type D(1)n

2006 ◽  
Vol 23 (4) ◽  
pp. 317-354 ◽  
Author(s):  
Anne Schilling ◽  
Philip Sternberg
Keyword(s):  
Quantum Affine Algebras ◽  
Type D ◽  
Finite Dimensional ◽  
Affine Algebras

scholarly journals Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I

2006 ◽  
Vol 184 ◽  
pp. 155-198 ◽  
Author(s):  
David Hernandez ◽  
Hiraku Nakajima
Keyword(s):  
Weight Module ◽  
Green Functions ◽  
Reductive Groups ◽  
Quantum Affine Algebras ◽  
Finite Dimensional ◽  
Affine Algebras

We study the monomial crystal defined by the second author. We show that each component of the monomial crystal can be embedded into a crystal of an extremal weight module introduced by Kashiwara. And we determine all monomials appearing in the components corresponding to all level 0 fundamental representations of quantum affine algebras except for some nodes of . Thus we obtain explicit descriptions of the crystals in these examples. We also give those for the corresponding finite dimensional representations. For classical types, we give them in terms of tableaux. For exceptional types, we list up all monomials.

scholarly journals Finite-dimensional representations of quantum affine algebras

1995 ◽  
Vol 28 (7) ◽  
pp. 1915-1927 ◽  
Author(s):  
G W Delius ◽  
Yao-Zhong Zhang
Keyword(s):  
Quantum Affine Algebras ◽  
Finite Dimensional ◽  
Affine Algebras

scholarly journals Representations of Quantum Affine Algebras in their R-Matrix Realization

2020 ◽  
Author(s):  
Naihuan Jing ◽  
◽  
Ming Liu ◽  
Alexander Molev ◽  
◽  
...  
Keyword(s):  
Irreducible Representations ◽  
Quantum Affine Algebras ◽  
R Matrix ◽  
Finite Dimensional ◽  
Gauss Decomposition ◽  
Affine Algebras

We use the isomorphisms between the R-matrix and Drinfeld presentations of the quantum affine algebras in types B, C and D produced in our previous work to describe finite-dimensional irreducible representations in the R-matrix realization.We also review the isomorphisms for the Yangians of these types and use Gauss decomposition to establish an equivalence of the descriptions of the representations in the R-matrix and Drinfeld presentations of the Yangians.

scholarly journals Level 0 Monomial Crystals

2006 ◽  
Vol 184 ◽  
pp. 85-153 ◽  
Author(s):  
David Hernandez ◽  
Hiraku Nakajima
Keyword(s):  
Weight Module ◽  
Quantum Affine Algebras ◽  
Finite Dimensional ◽  
Affine Algebras

We study the monomial crystal defined by the second author. We show that each component of the monomial crystal can be embedded into a crystal of an extremal weight module introduced by Kashiwara. And we determine all monomials appearing in the components corresponding to all level 0 fundamental representations of quantum affine algebras except for some nodes of . Thus we obtain explicit descriptions of the crystals in these examples. We also give those for the corresponding finite dimensional representations. For classical types, we give them in terms of tableaux. For exceptional types, we list up all monomials.

scholarly journals On finite-dimensional representations of two-parameter quantum affine algebras

2016 ◽  
Vol 15 (03) ◽  
pp. 1650054 ◽  
Author(s):  
Naihuan Jing ◽  
Honglian Zhang
Keyword(s):  
Irreducible Representations ◽  
Quantum Affine Algebras ◽  
Finite Dimensional ◽  
Affine Algebras ◽  
One To One ◽  
Two Parameter

We introduce the notion of Drinfeld polynomials of two-parameter quantum affine algebras and establish a one-to-one correspondence between finite-dimensional irreducible representations and sets of [Formula: see text]-tuples of pairs of polynomials with certain conditions.

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