AI 中文总结
该研究在D(2|1,α)电流代数导出范畴上构造三个导出自函子，证明其对应亏格二Macdonald算子，推导算子自伴随性与多项式正交性，完成亏格二DAHA的范畴化。
AI 中文摘要
我们在D(2|1,α)的平坦退化的电流代数的分次可积表示的导出范畴上构造三个导出自函子，并证明它们在Grothendieck群中的类是亏格二Macdonald算子；通过显式计算分次Ext配对，我们推导出亏格二Macdonald算子的自伴随性，以及亏格二Macdonald多项式关于某斜双线性形式的正交性。
英文摘要
We construct three derived endofunctors on the derived category of graded integrable representations of the current algebra of a flat degeneration of $D(2|1,α)$, and prove that their classes in the Grothendieck group are the genus two Macdonald operators. Computing the graded $\operatorname{Ext}$ pairing explicitly, we deduce the self-adjointness of the genus two Macdonald operators and the orthogonality of genus $2$ Macdonald polynomials with respect to the certain skew-bilinear form.
