The Lusztig automorphism of the q-Onsager algebra

2017/06/17 by Terwilliger, Paul
#33D80 #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1706.05546

Abstract

Pascal Baseilhac and Stefan Kolb recently introduced the Lusztig automorphism L of the q-Onsager algebra \mathcal O_q. In this paper, we express each of L, L^-1 as a formal sum involving some quantum adjoints. In addition, (i) we give a computer-free proof that L exists; (ii) we establish the higher order q-Dolan/Grady relations previously conjectured by Baseilhac and Thao Vu; (iii) we obtain a Lusztig automorphism for the current algebra \mathcal A_q associated with \mathcal O_q; (iv) we describe what happens when a finite-dimensional irreducible \mathcal O_q-module is twisted via L.

Related

• The S₃-symmetric q-Onsager algebra and its Lusztig automorphisms
• The Lusztig automorphism of U_q(\mathfraksl₂) from the equitable point of view
• The higher order q-Dolan-Grady relations and quantum integrable systems
• Twisting finite-dimensional modules for the q-Onsager algebra \mathcal O_q via the Lusztig automorphism
• A note on the O_q(sl₂) algebra