Junbin Dong

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math.RT2019

Geck's Conjecture and the Generalized Gelfand-Graev Representations in Bad Characteristic

Junbin Dong, Gao Yang

For a connected reductive algebraic group $G$ defined over a finite field $F_{q}$ , Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the…

math.RT2019

Alvis-Curtis Duality for Representations of Reductive Groups with Frobenius Maps

Junbin Dong

We generalize the Alvis-Curtis duality to the abstract representations of reductive groups with Frobenius maps. Similar to the case of representations of finite reductive groups, w…

math.RT2019

The Principal Representations of Reductive Algebraic Groups with Frobenius Maps

Junbin Dong

We introduce the principal representation category $O (G)$ of reductive algebraic groups with Frobenius maps and put forward a conjecture that this category is a hig…

math.RT2019

The Decomposition of Permutation Module for Infinite Chevalley Groups

Xiaoyu Chen, Junbin Dong

Let $G$ be a connected reductive group defined over $F_{q}$ , the finite field with $q$ elements. Let $B$ be an Borel subgroup defined over $F_{q}$ . In thi…

math.RT2018

Symmetric spaces associated to classical groups with even characteristic

Junbin Dong, Toshiaki Shoji, Gao Yang

Let $G = G L (V)$ for an N-dimensional vector space $V$ over an algebraically closed field k, and $G^{θ}$ the fixed point subgroup of $G$ under an involution $θ$ on $G$ . In the case wh…