Shuffle Approach Towards Quantum Affine and Toroidal Algebras by Alexander Tsymbaliuk

Author:Alexander Tsymbaliuk
Language: eng
Format: epub, pdf
ISBN: 9789819931507
Publisher: Springer Nature Singapore

so that

This implies (2.50).

Let so that of (2.3). Then:

due to (2.42) and . This implies a compatibility of (2.49) with (t2). The compatibility of (2.49) with the defining relations (, , ) is verified similarly.

To verify the compatibility with (t4), it suffices to note that

while applying (2.50) we also get

Finally, it is straightforward to check that for all r, hence, (t7 , t8 ) hold. This completes our proof of the Proposition.

Remark 2.7

Replacing with or in the formula (2.49) also gives rise to a -action on V(u).

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