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Extremal twist and tensor product of highest weight modules

journal contribution
posted on 2018-05-01, 09:27 authored by Andrey Mudrov
We give a criterion for complete reducibility of tensor product of two highest weight modules over a quantum group. It is found to be controlled by an extremal twist operator related to the Shapovalov inverse of either of the modules. As an application, we construct homogeneous vector bundles over quantum projective spaces $\mathbb{P}^n$ on $\mathbb{C}$-homs between certain parabolic Verma modules. Using an alternative realization of $\mathbb{C}_q[\mathbb{P}^n]$ as a subalgebra in $\mathbb{C}_q[GL(n+1)]$, we reformulate quantum vector bundles in terms of symmetric pairs. In this way, we prove complete reducibility of modules over the coideal stabilizer subalgebras, via the quantum Frobenius reciprocity.

History

Citation

Theoretical and Mathematical Physics, 2018, in press

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • AM (Accepted Manuscript)

Published in

Theoretical and Mathematical Physics

Publisher

Springer Verlag

issn

0040-5779

eissn

1573-9333

Copyright date

2018

Available date

2018-05-01

Publisher DOI

Notes

The file associated with this record is under embargo until 12 months after publication, in accordance with the publisher's self-archiving policy. The full text may be available through the publisher links provided above.

Language

en

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