Invariance of the Drinfeld pairing of a quantum group
Toshiyuki Tanisaki
TL;DR
This paper provides two new proofs demonstrating that the Drinfeld pairing remains invariant under braid group actions, utilizing different mathematical tools for each proof.
Contribution
It introduces alternative proofs of the invariance of the Drinfeld pairing, one via the Shapovalov form and another through the universal R-matrix.
Findings
Proves invariance of the Drinfeld pairing using the Shapovalov form.
Establishes invariance through characterization of the universal R-matrix.
Abstract
We give two alternative proofs of the invariance of the Drinfeld pairing under the action of the braid group. One uses the Shapovalov form, and the other uses a characterization of the universal -matrix.
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