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arXiv · 1207.2605

Quantum Affine Schubert Cells and FRT-Bialgebras: The E_6^{(1)} Case

Garrett Johnson·Christopher Nowlin
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Abstract

De Concini, Kac, and Procesi defined a family of subalgebras Uq[w] of the quantized enveloping algebra Uq(g) associated to elements w in the Weyl group of a simple Lie algebra g. These algebras are called quantum Schubert cell algebras. We show that, up to a mild cocycle twist, quotients of certain quantum Schubert cell algebras of types E_6 and E_6^{(1)} map isomorphically onto distinguished subalgebras of the Faddeev-Reshetikhin-Takhtajan universal bialgebra associated to the braiding on the quantum half-spin representation of Uq(so_{10}). We identify the quotients as those obtained by factoring out the quantum Schubert cell algebras by ideals generated by certain submodules with respect to the adjoint action of Uq(so_{10}).

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Garrett Johnson, Christopher Nowlin. 2012-07-11. Quantum Affine Schubert Cells and FRT-Bialgebras: The E_6^{(1)} Case. https://arxiv.org/abs/1207.2605

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