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Demazure Modules, Chari–Venkatesh Modules and Fusion Products
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Demazure Modules, Chari–Venkatesh Modules and Fusion Products
Інший ID:
2010 Mathematics Subject Classification: 17B67; 17B10
DOI:10.3842/SIGMA.2014.110
DOI:10.3842/SIGMA.2014.110
Посилання:
Demazure Modules, Chari–Venkatesh Modules and Fusion Products / B. Ravinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ.
Підтримка:
The author thanks Vyjayanthi Chari, K.N. Raghavan and S. Viswanath for many helpful discussions
and encouragement. Part of this work was done when the author was visiting the Centre de
Recherche Mathematique (CRM), Montreal, Canada, during the thematic semester on New Directions
in Lie Theory. The author acknowledges the hospitality and financial support extended
to him by CRM. The author also thanks the anonymous referees for their valuable comments,
due to which the paper is much improved. The author acknowledges support from CSIR under
the SPM Fellowship scheme
Дата:
2014
Переглядів:
544
Завантажень:
245
Анотація:
Let g be a finite-dimensional complex simple Lie algebra with highest root θ. Given two non-negative integers m, n, we prove that the fusion product of m copies of the level one Demazure module D(1,θ) with n copies of the adjoint representation ev₀V(θ) is independent of the parameters and we give explicit defining relations. As a consequence, for g simply laced, we show that the fusion product of a special family of Chari-Venkatesh modules is again a Chari-Venkatesh module. We also get a description of the truncated Weyl module associated to a multiple of θ.
