Categorical relations between Langlands dual quantum affine algebras: doubly laced types
We prove that the Grothendieck rings of category C Q ( t ) over quantum affine algebras U q ′ ( g ( t ) ) ( t = 1 , 2 ) associated with each Dynkin quiver Q of finite type A 2 n - 1 (resp. D n + 1 ) are isomorphic to one of the categories C Q over the Langlands dual U q ′ ( L g ( 2 ) ) of U q ′ ( g...
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| Veröffentlicht in: | Journal of algebraic combinatorics 2019-06, Vol.49 (4), p.401-435 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We prove that the Grothendieck rings of category
C
Q
(
t
)
over quantum affine algebras
U
q
′
(
g
(
t
)
)
(
t
=
1
,
2
)
associated with each Dynkin quiver
Q
of finite type
A
2
n
-
1
(resp.
D
n
+
1
) are isomorphic to one of the categories
C
Q
over the Langlands dual
U
q
′
(
L
g
(
2
)
)
of
U
q
′
(
g
(
2
)
)
associated with any twisted adapted class
[
Q
]
of
A
2
n
-
1
(resp.
D
n
+
1
). This results provide simplicity-preserving correspondences on Langlands duality for finite-dimensional representation of quantum affine algebras, suggested by Frenkel–Hernandez. |
|---|---|
| ISSN: | 0925-9899 1572-9192 |
| DOI: | 10.1007/s10801-018-0829-z |