scholarly journals Cluster algebras and category 𝒪 for representations of Borel subalgebras of quantum affine algebras

2016 ◽  
Vol 10 (9) ◽  
pp. 2015-2052 ◽  
Author(s):  
David Hernandez ◽  
Bernard Leclerc
Keyword(s):  
Cluster Algebras ◽  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals Cluster algebras and quantum affine algebras

2010 ◽  
Vol 154 (2) ◽  
pp. 265-341 ◽  
Author(s):  
David Hernandez ◽  
Bernard Leclerc
Keyword(s):  
Cluster Algebras ◽  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras

2020 ◽  
Author(s):  
Fan Qin ◽  
Keyword(s):  
Cluster Algebras ◽  
Quantum Affine Algebras ◽  
Simple Modules ◽  
Canonical Bases ◽  
Affine Algebras ◽  
Quantum Cluster

Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the dual canonical bases of quantum unipotent subgroups. It also applies to the t-analogs of q-characters of simple modules of quantum affine algebras.

Quantum affine algebras

1991 ◽  
Vol 142 (2) ◽  
pp. 261-283 ◽  
Author(s):  
Vyjayanthi Chari ◽  
Andrew Pressley
Keyword(s):  
Quantum Affine Algebras ◽  
Affine Algebras

Standard modules of quantum affine algebras

2002 ◽  
Vol 111 (3) ◽  
pp. 509-533 ◽  
Author(s):  
E. Vasserot ◽  
M. Varagnolo
Keyword(s):  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals Symmetric quiver Hecke algebras andR-matrices of quantum affine algebras III: Table 1.

2015 ◽  
Vol 111 (2) ◽  
pp. 420-444 ◽  
Author(s):  
Seok-Jin Kang ◽  
Masaki Kashiwara ◽  
Myungho Kim ◽  
Se-jin Oh
Keyword(s):  
Hecke Algebras ◽  
Quantum Affine Algebras ◽  
Affine Algebras

scholarly journals Categories over quantum affine algebras and monoidal categorification

2021 ◽  
Vol 97 (7) ◽  
Author(s):  
Masaki Kashiwara ◽  
Myungho Kim ◽  
Se-jin Oh ◽  
Euiyong Park
Keyword(s):  
Quantum Affine Algebras ◽  
Affine Algebras
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