Limit multiplicities for ${\mathrm {SL}}_2(\mathcal{O}_F)$ in ${\mathrm {SL}}_2(\mathbb{R}^{r_1}\oplus\mathbb{C}^{r_2})$

Jasmin Matz

doi:10.4171/ggd/507

Limit multiplicities for $SL_{2} (O_{F})$ in $SL_{2} (R^{r_{1}} \oplus C^{r_{2}})$

Jasmin Matz
The Hebrew University of Jerusalem, Israel

$Limit multiplicities for ${\mathrm {SL}}_2(\mathcal{O}_F)$ in ${\mathrm {SL}}_2(\mathbb{R}^{r_1}\oplus\mathbb{C}^{r_2})$ cover$

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Abstract

We prove that the family of lattices $SL_{2} (O_{F})$ , $F$ running over number fields with fixed archimedean signature $(r_{1}, r_{2})$ , in $SL_{2} (R^{r_{1}} \oplus C^{r_{2}})$ has the limit multiplicity property.

Cite this article

Jasmin Matz, Limit multiplicities for $SL_{2} (O_{F})$ in $SL_{2} (R^{r_{1}} \oplus C^{r_{2}})$ . Groups Geom. Dyn. 13 (2019), no. 3, pp. 841–881

DOI 10.4171/GGD/507