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UBC Theses and Dissertations

Shifted q = 0 affine algebras Hsu, You-Hung


In this thesis, we accomplish the following three things. 1. Defining the shifted q = 0 affine algebras (Chapter 2). 2. Explaining what it means for such algebra to act on categories (Chapter 3). 3. Giving an example of such a categorical action (Chapter 5). Our motivation comes from the categorification of quantum groups and their action on categories. On the derived categories of coherent sheaves on Grassmannians or partial flag varieties, we try to understand an action via using the language of Fourier-Mukai transformations with kernels inducing by natural correspondences. After decategorifying, the q = 0 shifted affine algebras are similar to the shifted quantum affine algebras defined by Finkelberg-Tsymbaliuk [FT], where some of the relations can be obtained from their relations by taking v = 0 (i.e. the q-analogue). Finally, we relate shifted q = 0 affine algebras to q = 0 affine Hecke algebras. In particular, we use the action of shifted q = 0 affine algebras to construct an action of the q = 0 affine Hecke algebras on the derived category of coherent sheaves on full flag varieties. We also relate this action to the notion of Demazure descent which was introduced in [AK1].

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