Weights of mixed tilting sheaves and geometric Ringel duality |
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Authors: | Zhiwei Yun |
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Institution: | (1) Department of Mathematics, Princeton University, Princeton, NJ, 08544, U.S.A |
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Abstract: | We describe several general methods for calculating weights of mixed tilting sheaves. We introduce a notion called “non-cancellation
property” which implies a strong uniqueness of mixed tilting sheaves and enables one to calculate their weights effectively.
When we have a certain Radon transform, we prove a geometric analogue of Ringel duality which sends tilting objects to projective
objects. We apply these methods to (partial) flag varieties and affine (partial) flag varieties and show that the weight polynomials
of mixed tilting sheaves on flag and affine flag varieties are essentially given by Kazhdan-Lusztig polynomials. This verifies
a mixed geometric analogue of a conjecture by W. Soergel in 10].
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 14F20 Secondary 14L30 20G25 |
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