Zhe Chen

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20232025

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math.RT2025

Class numbers and invariant characters of $sl_{2} (F_{p})$

Zhe Chen, Yongqi Feng

Let $p$ be a prime and let $S_{2} (Γ (p))$ be the space of weight $2$ cusp forms for the principal congruence subgroup $Γ (p)$ . Then $SL_{2} (F_{p})$ acts on $S_{2} (Γ (p))$ in…

math.RT2024

A remark on decomposing the canonical representation of the Drinfeld curve

Zhe Chen, Yushan Pan

Recently, by studying an explicit basis, Köck and Laurent give the decomposition of the $F_{q} [SL_{2} (F_{q})]$ -module of holomorphic forms on the Dr…

math.RT2024

Hopf algebra and the duality operation for $gl_{n} (F_{q})$

Zhe Chen

In this paper we study the space $C (gl_{n} (F_{q}))$ of complex invariant functions on $gl_{n} (F_{q})$ , through a Hopf algebra viewpoint. First, we c…

math.RT2023

The algebraisation of higher level Deligne--Lusztig representations II: odd levels

Zhe Chen, Alexander Stasinski

In this paper we study higher level Deligne--Lusztig representations of reductive groups over discrete valuation rings, with finite residue field $F_{q}$ . In previous work w…

Class numbers and invariant characters of sl2​(Fp​)

A remark on decomposing the canonical representation of the Drinfeld curve

Hopf algebra and the duality operation for gln​(Fq​)

The algebraisation of higher level Deligne--Lusztig representations II: odd levels

Class numbers and invariant characters of $sl_{2} (F_{p})$

Hopf algebra and the duality operation for $gl_{n} (F_{q})$