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Xue‐Yi Ma

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Preprint Oct 2026

Invariant Measures on Smooth Algebraic Groups over Higher Local Fields

We construct a positive, finitely additive, left-invariant measure on the congruence cylinder ring of a smooth $d$-dimensional algebraic group over an $n$-dimensional local field. The measure takes values in $\mathbb{R}((X_2))\cdots((X_n))$. A normalized cylinder of depth $(i_1,\ldots,i_n)$ has volume $q^{-di_1}\prod_{...

Xue-Yi Ma, Jing-Wen Zhu · 0 citations

Preprint Aug 2026

The principal series 2-representation for $\mathrm{GL}_n\times\mathrm{GL}_n$ over a 2-dimensional local field

Let $F=\mathbb{F}_q((u))((t))$ and $H=\mathrm{GL}_n(F)_L\times\mathrm{GL}_n(F)_R$. An ordered tuple $\alpha=(\alpha_1,\dots, \alpha_n) $ defines a cross-$K_2$ multiplier on the doubled Borel. Twisted equivariantization then yields an exact uniformly smooth categorical principal series $2$-representation of $H$. For uni...

Xue-Yi Ma, Jing-Wen Zhu · 0 citations