Differential Equations on Hyperplane Complements
نویسنده
چکیده
The goal of the next two talks is to (1) discuss a class of integrable connections associated to root systems (2) describe their monodromy in terms of quantum groups These connections come in two forms: • Rational form leading to representations of braid groups (this week) • Trigonometric form leading to representations of affine braid groups (next week) The relevance of these connections is that A: the quantum differential equations for Nakajima quiver varieties are of trigonometric type B: the description of their monodromy in terms of quantum groups constitutes a step towards proving Roman Bezrukanikov’s conjectures that the monodromy lifts to/comes from a braid group action on the derived category.
منابع مشابه
Differential Equations on Hyperplane Complements Ii
1.2. Let E be a Euclidean vector space, Φ ⊂ E∗ a root system. Denote Q ⊂ h∗ the root lattice, and P ⊂ h∗ the weight lattice. Let Q∨ ⊂ E be the lattice generated by the coroots α∨, α ∈ Φ, the coroot lattice is dual to the weight lattice P ⊂ h∗, and P∨ ⊂ E the dual weight lattice, which is dual to the root lattice Q. Let H = HomZ(P,C) = Q∨ ⊗Z C∗ be the complex algebraic torus with Lie algebra h =...
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Suppose ∆ is a dual polar space of rank n and H is a hyperplane of ∆. Cardinali, De Bruyn and Pasini have already shown that if n ≥ 4 and the line size is greater than or equal to four then the hyperplane complement ∆ − H is simply connected. Shpectorov proved a similar result for n ≥ 3 and line size five and above. We will prove a similar result for n ≥ 5 and line size three and above. We also...
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