Extremal loop weight modules and tensor products for quantum toroidal algebras

@inproceedings{Mansuy2013ExtremalLW,
title={Extremal loop weight modules and tensor products for quantum toroidal algebras},
author={Mathieu Mansuy},
year={2013}
}
• Mathieu Mansuy
• Published 2013
• Mathematics
• We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by Feigin-Jimbo-Miwa-Mukhin [6] and constructed by the author [21] as a subfamily of extremal loop weight modules. In addition we get new extremal loop weight modules as subquotients of tensor powers of vector representations. As an application we obtain finite-dimensional representations of quantum… CONTINUE READING

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Extremal loop weight modules for $U_q(\hat{sl}_\infty)$

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CITES BACKGROUND, RESULTS & METHODS

References

Publications referenced by this paper.
SHOWING 1-10 OF 28 REFERENCES

QUANTUM EXTREMAL LOOP WEIGHT MODULES AND MONOMIAL CRYSTALS

VIEW 10 EXCERPTS

Representations of quantum toroidal gln

• Mathematics
• 2012
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

The algebra Uq(slˆ∞) and applications

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Crystal bases and two-sided cells of quantum affine algebras

• Mathematics
• 2002
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

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

• Mathematics, Physics
• 1998
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Crystal bases of modified quantized enveloping algebra

VIEW 14 EXCERPTS
HIGHLY INFLUENTIAL

Quantum toroidal algebras and their representations

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Drinfeld coproduct, quantum fusion tensor category and applications

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Representations of Quantum Affinizations and Fusion Product

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

On level-zero representation of quantized affine algebras

VIEW 13 EXCERPTS
HIGHLY INFLUENTIAL