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- W2945011538 abstract "For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this property, then we call it a Borel subalgebra. Besides the positive part of the quantum group and its reflections, we find new unfamiliar Borel subalgebras, for example ones containing copies of the quantum Weyl algebra. Given a Borel subalgebra, we study its induced (Verma-)modules and prove among others that they have all irreducible finite-dimensional modules as quotients. We then give structural results using the graded algebra, which in particular leads to a conjectural formula for all triangular Borel subalgebras, which we partly prove. As examples, we determine all Borel subalgebras of $U_q(mathfrak{sl}_2)$ and $U_q(mathfrak{sl}_3)$ and discuss the induced modules." @default.
- W2945011538 created "2019-05-29" @default.
- W2945011538 creator A5028436092 @default.
- W2945011538 creator A5040825241 @default.
- W2945011538 date "2019-05-14" @default.
- W2945011538 modified "2023-10-16" @default.
- W2945011538 title "On Borel subalgebras of quantum groups" @default.
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