Higher Sugawara Operators for the Quantum Affine Algebras of Type A

Frappat, Luc; Jing, Naihuan; Molev, Alexander; Ragoucy, Eric

doi:10.1007/s00220-015-2566-7

Higher Sugawara Operators for the Quantum Affine Algebras of Type A

Luc Frappat
(
- Annecy, LAPTH
)
,
Naihuan Jing
(
- South China U. Tech. and
- NCSU, Raleigh, Dept. Math.
)
,
Alexander Molev
(
- U. Sydney (main)
)
,
Eric Ragoucy
(
- Annecy, LAPTH
)

May 14, 2015

27 pages

Published in:

Commun.Math.Phys. 345 (2016) 2, 631-657

Published: Jan 11, 2016

e-Print:

1505.03667 [math.QA]

DOI:

10.1007/s00220-015-2566-7

Report number:

LAPTH-027-15

View in:

pdf

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Abstract: (Springer)

We give explicit formulas for the elements of the center of the completed quantum affine algebra in type A at the critical level that are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the q-deformed classical

{{\mathcal W}}

-algebra of Frenkel and Reshetikhin.

Note:

32 pages

algebra: affine
algebra: deformation
algebra: W
R-matrix

References(28)

Figures(0)

[1]

Free boson realization of U-q(sl(N)

- Commun.Math.Phys. 162 (1994) 61-84
•
e-Print:
- hep-th/9305146
•
DOI:
- 10.1007/BF02105187

[2]

Convex bases of PBW type for quantum affine algebras

Jonathan Beck
(
- MIT
)

- Commun.Math.Phys. 165 (1994) 193-200
•
e-Print:
- hep-th/9407003
•
DOI:
- 10.1007/BF02099742

[3]

Braid group action and quantum affine algebras

Jonathan Beck
(
- MIT
)

- Commun.Math.Phys. 165 (1994) 555-568
•
e-Print:
- hep-th/9404165
•
DOI:
- 10.1007/BF02099423

[4]

Parabolic presentations of the Yangian Y(gln)

J. Brundan
,
A. Kleshchev

- Commun.Math.Phys. 254 (2005) 191-220

[5]

A new interpretation of Gelfand-Tzetlin bases

I.V. Cherednik

- Duke Math.J. 54 (1987) 563-577

[6]

Algebraic properties of Maninmatrices II: q-analogues and integrable systems

A. Chervov
,
G. Falqui
,
V. Rubtsov
,
A. Silantyev

- Adv.Appl.Math. 60 (2014) 25-89

[7]

On higher order Sugawara operators

A.V. Chervov
,
A.I. Molev

- Int.Math.Res.Not. 9 (2009) 1612-1635

[8]

Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence

A. Chervov
(
- Moscow, ITEP
)
,
D. Talalaev
(
- Moscow, ITEP
)

e-Print:
- hep-th/0604128

[9]

The center of a quantum affine algebra at the critical level

J. Ding
,
P. Etingof

- Math.Res.Lett. 1 (1994) 469-480

[10]

Isomorphism of two realizations of quantum affine algebra Uq(glb

J. Ding
,
I.B. Frenkel

- Commun.Math.Phys. 156 (1993) 277-300

[11]

A New realization of Yangians and quantized affine algebras

V.G. Drinfeld

- Sov.Math.Dokl. 36 (1988) 212-216

[12]

Quantization of Lie bialgebras. V. Quantum vertex operator algebras, Selecta Math. (N.S.) 6 , 105-130

P. Etingof
,
D. Kazhdan

[13]

Gaudin model, Bethe ansatz and correlation functions at the critical level

Boris Feigin
(
- Landau Inst.
)
,
Edward Frenkel
(
- Harvard U.
)
,
Nikolai Reshetikhin
(
- UC, Berkeley, Math. Dept.
)

- Commun.Math.Phys. 166 (1994) 27-62
•
e-Print:
- hep-th/9402022
•
DOI:
- 10.1007/BF02099300

[14]

Gaudin models with irregular singularities

- Adv.Math. 223 (2010) 873-948
•
e-Print:
- math/0612798
•
DOI:
- 10.1016/j.aim.2009.09.007

[15]

Langlands correspondence for loop groups, Cambridge Studies in Advanced Mathematics, 103. Cambridge University Press, Cambridge

E. Frenkel

[16]

The Hopf algebra Rep Uqglb∞

E. Frenkel
,
E. Mukhin

- Selecta Math. 8 (2002) 537-635

[17]

Quantum affine algebras and deformations of Virasoro and W-algebras

E. Frenkel
,
N. Reshetikhin

- Commun.Math.Phys. 178 (1996) 237-264

[18]

The q-characters of representations of quantum affine algebras and deformations of W-algebras

E. Frenkel
,
N. Reshetikhin

- Contemp.Math. 248 (1999) 163-205

[19]

Vertex representations of quantum affine algebras

I.B. Frenkel
,
N. Jing

- Proc.Nat.Acad.Sci. 85 (1988) 9373-9377

[20]

Quantum affine algebras and holonomic difference equations

I.B. Frenkel
(
- Yale U.
)
,
N.Yu. Reshetikhin
(
- UC, Berkeley
)

- Commun.Math.Phys. 146 (1992) 1-60
•
DOI:
- 10.1007/BF02099206

[21]

Representations of twisted q-Yangians, Selecta Math., New Series 16 , 439-499

L. Gow
,
A. Molev

[22]

A q-analogue of the centralizer construction and skew representations of the quantum affine algebra, Symmetry, Integrability and Geometry:Methods and Applications 2 , paper 092, 29 pp

M.J. Hopkins
,
A.I. Molev

[23]

Yangians and classical Lie algebras, Mathematical Surveys and Monographs,143. American Mathematical Society, Providence, RI

A. Molev

[24]

Period Integrals of CY and General Type Complete Intersections

Bong H. Lian
(
- Brandeis U.
)
,
Shing-Tung Yau
(
- Harvard U., Dept. Math.
)

- Invent.Math. 191 (2013) 1
•
e-Print:
- 1105.4872
•
DOI:
- 10.1007/s00222-012-0391-6

[25]

Conformal field theory, automorphic forms and related topics

A.I. Molev
,
E.E. Mukhin

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