Isomorphism between the $R$-Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$ - INSPIRE

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Isomorphism between the $R$ -Matrix and Drinfeld Presentations of Quantum Affine Algebra: Types $B$ and $D$

2020

Published in:

SIGMA 16 (2020) 043

Published: 2020

DOI:

10.3842/SIGMA.2020.043

View in:

AMS MathSciNet

reference search16 citations

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Abstract: (SIGMA)

Following the approach of Ding and Frenkel [Comm. Math. Phys. 156 (1993), 277-300] for type

A

, we showed in our previous work [J. Math. Phys. 61 (2020), 031701, 41 pages] that the Gauss decomposition of the generator matrix in the

R

-matrix presentation of the quantum affine algebra yields the Drinfeld generators in all classical types. Complete details for type

C

were given therein, while the present paper deals with types

B

and

D

. The arguments for all classical types are quite similar so we mostly concentrate on necessary additional details specific to the underlying orthogonal Lie algebras.

$R$ -matrix presentation
Drinfeld new presentation
universal $R$ -matrix
Gauss decomposition.

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