Séminaire Lotharingien de Combinatoire, 95B.40 (2026), 12 pp.

Ruizhen Liu

Deligne-Lusztig Varieties, Toric Orbifolds, and the q-Klyachko Algebra

Abstract. We investigate the geometry of the q-Klyachko algebra in the sense of Nadeau-Tewari. When q is a prime power, we show that the q-Klyachko algebra is the image of the pullback map on Chow rings CH(Fl_n+1) → CH(DL_n), where DL_n is a compactified Deligne-Lusztig variety inside the complete flag variety Fl_n+1. When q is a positive rational number, we establish a Kähler package for the q-Klyachko algebra through inputs from toric geometry.

Received: November 15, 2025. Accepted: February 15, 2026. Final version: April 1, 2026.

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