论文标题
算术表示实际上是自由群体的增长
Arithmetic Representation Growth of Virtually Free Groups
论文作者
论文摘要
我们从Quiver代表理论和Hall代数技术中调整方法，以计算实际上自由群体在有限领域上的表示。这引起了$ \ mathbf {gl} _d（\ Mathbb {c}）$ - 几乎免费组的字符品种的计算。作为示例，我们讨论了$ \ mathbb {d} _ \ infty $，$ \ mathbf {psl} _2（\ Mathbb {z}）$，$ \ Mathbf {slbf {sl} _2 _2 _2（\ Mathbb {z}）$，$ \ MathBf {$ \ m i { $ \ mathbf {pgl} _2（\ mathbb {z}）$。
We adapt methods from quiver representation theory and Hall algebra techniques to the counting of representations of virtually free groups over finite fields. This gives rise to the computation of the E-polynomials of $\mathbf{GL}_d(\mathbb{C})$-character varieties of virtually free groups. As examples we discuss the representation theory of $\mathbb{D}_\infty$ , $\mathbf{PSL}_2(\mathbb{Z})$ , $\mathbf{SL}_2(\mathbb{Z})$ , $\mathbf{GL}_2(\mathbb{Z})$ and $\mathbf{PGL}_2(\mathbb{Z})$ .
