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A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra
Інший ID:
2000 Mathematics Subject Classification: 81R10
Посилання:
A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra / M.J. Hopkins, A.I. Molev // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ.
Підтримка:
This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. We would like to thank Boris Feigin for discussions and Serge Ovsienko for help with the proof
of Theorem 5.4.
Дата:
2006
Переглядів:
792
Завантажень:
278
Анотація:
We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or q-character). We also apply the quantum Sylvester theorem to construct a q-analogue of the Olshanski algebra as a projective limit of certain centralizers in Uq(gln) and show that this limit algebra contains the q-Yangian as a subalgebra.
