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

@inproceedings{Mansuy2013ExtremalLW, title={Extremal loop weight modules for \$U_q(\hat\{sl\}_\infty)\$}, author={Mathieu Mansuy}, year={2013} }

We construct by fusion product new irreducible representations of the quantum affinization $U_q(\hat{sl}_\infty)$. The action is defined via the Drinfeld coproduct and is related to the crystal structure of semi-standard tableaux of type $A_\infty$. We call these representations extremal loop weight modules. The main motivations are applications to quantum toroidal algebras $U_q(sl_{n+1}^{tor})$: we prove the conjectural link between $U_q(\hat{sl}_\infty)$ and $U_q(sl_{n+1}^{tor})$ stated in… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 26 REFERENCES

## QUANTUM EXTREMAL LOOP WEIGHT MODULES AND MONOMIAL CRYSTALS

VIEW 8 EXCERPTS

## The algebra Uq(slˆ∞) and applications

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Crystal bases of modified quantized enveloping algebra

VIEW 16 EXCERPTS

HIGHLY INFLUENTIAL

## Representations of quantum toroidal gln

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## On level-zero representation of quantized affine algebras

VIEW 11 EXCERPTS

HIGHLY INFLUENTIAL

## Quiver varieties and finite dimensional representations of quantum affine algebras

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

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

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Quantum toroidal algebras and their representations

VIEW 1 EXCERPT