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- W2964202112 abstract "We consider all Bott-Samelson varieties BS(s) for a fixed connected semisimple complex algebraic group with maximal torus T as the class of objects of some category. The class of morphisms of this category is an extension of the class of canonical (inserting the neutral element) morphisms BS(s)↪BS(s′), where s is a subsequence of s′. Every morphism of the new category induces a map between the T-fixed points but not necessarily between the whole varieties. We construct a contravariant functor from this new category to the category of graded (phantom {dot {i}!}H^{bullet }_{T}(text {pt}))-modules coinciding on the objects with the usual functor (phantom {dot {i}!}H_{T}^{bullet }) of taking T-equivariant cohomologies. We also discuss the problem how to define a functor to the category of T-spaces from a smaller subcategory. The exact answer is obtained for groups whose root systems have simply laced irreducible components by explicitly constructing morphisms between Bott-Samelson varieties (different from the canonical ones)." @default.
- W2964202112 created "2019-07-30" @default.
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- W2964202112 date "2019-01-10" @default.
- W2964202112 modified "2023-09-24" @default.
- W2964202112 title "Categories of Bott-Samelson Varieties" @default.
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- W2964202112 doi "https://doi.org/10.1007/s10468-018-09852-6" @default.
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