Products of conjugacy classes in $\mathrm{SL}_2(\mathbb{R})$
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 1, pp. 87-96.

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We compute the product of any $ n$-tuple of conjugacy classes in $ \mathrm {SL}_2(\mathbb{R})$.
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S. Yu. Orevkov. Products of conjugacy classes in $\mathrm{SL}_2(\mathbb{R})$. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/MMO_2019_80_1_a2/

[1] Agnihotri S., Woodward C., “Eigenvalues of products of unitary matrices and quantum Schubert calculus”, Math. Res. Lett., 5:6 (1998), 817–836 | DOI | MR | Zbl

[2] Arad Z., Herzog M. (eds.), Products of conjugacy classes in groups, Lect. Notes in Math., 1112, Springer, Berlin, 1985 | DOI | MR | Zbl

[3] Artal E., Carmona J., Cogolludo J. I., “Effective invariants of braid monodromy”, Trans. AMS, 359:1 (2007), 165–183 | DOI | MR | Zbl

[4] Belkale P., “Local systems on $\mathbb P^1-S$ for $S$ a finite set”, Compos. Math., 129:1 (2001), 67–86 | DOI | MR | Zbl

[5] Brenner J. L., “Covering theorems for nonabelian simple groups, IV”, Jñānābha Sect. A, 3 (1973), 77–84 | MR | Zbl

[6] Falbel E., Wentworth R. A., “On products of isometries of hyperbolic space”, Topology Appl., 156:13 (2009), 2257–2263 | DOI | MR | Zbl

[7] García-Prada O., Logares M., Muñoz V., “Moduli spaces of parabolic $\mathrm U(p,q)$-Higgs bundles”, Q. J. Math., 60:2 (2009), 183–233 | DOI | MR | Zbl

[8] Gordeev N. L., “Products of conjugacy classes in perfect linear groups. Extended covering number”, Zapiski nauchn. sem. POMI, 321, 2005, 67–89 | MR | Zbl

[9] Karni S., “Covering numbers of groups of small order and sporadic groups”, Products of conjugacy classes in groups, Lect. Notes in Math., 1112, Springer, Berlin, 1985, 52–196 | DOI | MR

[10] Liebeck M. W., Shalev A., “Diameters of finite simple groups: sharp bounds and applications”, Ann. of Math. (2), 154:2 (2001), 383–406 | DOI | MR | Zbl

[11] Orevkov S. Yu., “Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves”, J. Knot Theory Ramifications, 10:7 (2001), 1005–1023 | DOI | MR | Zbl

[12] Orevkov S. Yu., “Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$”, Ann. Fac. Sci. Toulouse. Math. (6), 22:2 (2013), 219–251 | DOI | MR | Zbl

[13] Paupert J., “Elliptic triangle groups in $PU(2,1)$, Lagrangian triples and momentum maps”, Topology, 46:2 (2007), 155–183 | DOI | MR | Zbl

[14] Paupert J., Will P., “Involution and commutator length for complex hyperbolic isometries”, Michigan Math. J., 66:4 (2017), 699–744 | DOI | MR | Zbl

[15] Simpson C., “Products of matrices”, Differential geometry, global analysis, and topology (Halifax, NS, 1990), CMS Conf. Proc., 12, AMS, Providence, RI, 1991, 157–185 | MR