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arxiv: 1403.5570 · v2 · pith:PYZZVII3new · submitted 2014-03-21 · 🧮 math.RT · math.QA

Quantum Satake in type A: part I

Ben Elias This is my paper
classification 🧮 math.RT math.QA
keywords casebimodulescertainequivalenceprovesatakesingularsoergel
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We give an interpretation of sl_n webs as morphisms between certain singular Soergel bimodules. We explain how this is a combinatorial, algebraic version of the geometric Satake equivalence (in type A). We then q-deform the construction, giving an equivalence between representations of U_q(sl_n) and certain singular Soergel bimodules for a q-deformed Cartan matrix. In this paper, we discuss the general case but prove only the case n=2,3. In the sequel we will prove the case n >= 4.

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