The trigonometric Casimir connection of a simple Lie algebra

Abstract

Let g be a complex, semisimple Lie algebra, G the corresponding simply-connected Lie group and H a maximal torus in G. We construct a flat connection on H with logarithmic singularities on the root hypertori and values in the Yangian Y(g) of g. By analogy with the rational Casimir connection of g, we conjecture that the monodromy of this trigonometric connection is described by the quantum Weyl group operators of the quantum loop algebra U_h(Lg).

44 pages. Some typos corrected and minor changes made. Final version to appear in the Journal of Algebra

References in corpus (3)

• Parabolic presentations of the Yangian Y(gl_n)
• Bethe Subalgebras in Twisted Yangians
• Dynamical differential equations compatible with rational qKZ equations

Cited by in corpus (13)

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• Hypergeometric solutions of the quantum differential equation of the cotangent bundle of a partial flag variety
• Degeneration of trigonometric dynamical difference equations for quantum loop algebras to trigonometric Casimir equations for Yangians
• The elliptic Casimir connection of a simple Lie algebra
• On deformed double current algebras for simple Lie algebras
• Universal KZB Equations for arbitrary root systems
• Generalized theta series and monodromy of Casimir connection. The case of rank 1
• The Dynamical equations for $\mathfrak{gl}(n|m)$
• Quantum differential and difference equations for ${\mathrm{Hilb}}^n({\mathbb{C}}^2)$