Polishchuk’s conjecture and Kazhdan–Laumon representations

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Polishchuk's conjecture is proven for all types, confirming Kazhdan and Laumon's well-defined construction.
The counterexample by Bezrukavnikov and Polishchuk highlights the shortcomings in the original construction framework.
A graded version of the Grothendieck group can generate finite projective dimension modules, supporting the conjecture's viability.
The implications affect discrete series representations of Chevalley groups over finite fields, enhancing representation theory.

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Analysis demonstrates Polishchuk's conjecture validates Kazhdan-Laumon representations in finite fields, suggesting new constructions.

Calder Morton-Ferguson (2025) studied this question.

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