论文标题
紧凑的特殊线性二级线性群的表示形式
Construction of representations of compact special linear groups of degree two
论文作者
论文摘要
我们在紧凑的离散估值环上构建了$ \ mathrm {sl} _2 $的有限尺寸连续复杂表示。我们还证明，这种紧凑的离散估值环的$ \ mathrm {sl} _2 $的复杂组代数_2 $取决于环的特征。特别是，我们证明了组代数$ \ mathbb {c} [\ mathrm {sl} _2（\ Mathbb {Z}/2^r \ Mathbb {z}）$和$ \ Mathbb {c} c} c}对于任何$ r \ geq 4而不是同构。$
We construct the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over compact discrete valuation rings of even residual characteristic. We also prove that the complex group algebras of $\mathrm{SL}_2$ over finite quotient rings of such compact discrete valuation rings depend on the characteristic of the ring. In particular, we prove that the group algebras $\mathbb{C}[\mathrm{SL}_2 (\mathbb{Z}/2^r \mathbb{Z})]$ and $\mathbb{C}[\mathrm{SL}_2 (\mathbb{F}_2 [t]/(t^r ))]$ are not isomorphic for any $r\geq 4.$
