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A categorical action of the shifted
$0$-affine algebra
- Part of
-
- Journal:
- Forum of Mathematics, Sigma / Volume 13 / 2025
- Published online by Cambridge University Press:
- 15 April 2025, e74
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- Article
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We introduce a new algebra
$\mathcal {U}=\dot {\mathrm {\mathbf{U}}}_{0,N}(L\mathfrak {sl}_n)$ called the shifted 
$0$-affine algebra, which emerges naturally from studying coherent sheaves on n-step partial flag varieties through natural correspondences. This algebra 
$\mathcal {U}$ has a similar presentation to the shifted quantum affine algebra defined by Finkelberg-Tsymbaliuk. Then, we construct a categorical 
$\mathcal {U}$-action on a certain 2-category arising from derived categories of coherent sheaves on n-step partial flag varieties. As an application, we construct a categorical action of the affine 
$0$-Hecke algebra on the bounded derived category of coherent sheaves on the full flag variety.
