Products of conjugacy classes in 𝑆𝐿₂(ℝ)

Orevkov, S.

doi:10.1090/mosc/287

Products of conjugacy classes in $\mathrm {SL}_2(\mathbb {R})$
HTML articles powered by AMS MathViewer

by S. Yu. Orevkov
Translated by: S. Yu. Orevkov

Trans. Moscow Math. Soc. 2019, 73-81

DOI: https://doi.org/10.1090/mosc/287

Published electronically: March 31, 2020

PDF | Request permission

Abstract:

We compute the product of any $n$-tuple of conjugacy classes in $\mathrm {SL}_2(\mathbb {R})$.

References

S. Agnihotri and C. Woodward, Eigenvalues of products of unitary matrices and quantum Schubert calculus, Math. Res. Lett. 5 (1998), no. 6, 817–836. MR 1671192, DOI 10.4310/MRL.1998.v5.n6.a10
Z. Arad and M. Herzog (eds.), Products of conjugacy classes in groups, Lecture Notes in Mathematics, vol. 1112, Springer-Verlag, Berlin, 1985. MR 783067, DOI 10.1007/BFb0072284
Enrique Artal Bartolo, Jorge Carmona Ruber, and José Ignacio Cogolludo Agustín, Effective invariants of braid monodromy, Trans. Amer. Math. Soc. 359 (2007), no. 1, 165–183. MR 2247887, DOI 10.1090/S0002-9947-06-03881-5
Prakash Belkale, Local systems on $\Bbb P^1-S$ for $S$ a finite set, Compositio Math. 129 (2001), no. 1, 67–86. MR 1856023, DOI 10.1023/A:1013195625868
J. L. Brenner, Covering theorems for nonabelian simple groups. IV, Jñānābha Sect. A 3 (1973), 77–84. MR 346044
Elisha Falbel and Richard A. Wentworth, On products of isometries of hyperbolic space, Topology Appl. 156 (2009), no. 13, 2257–2263. MR 2544135, DOI 10.1016/j.topol.2009.05.013
O. García-Prada, M. Logares, and Vicente Muñoz, Moduli spaces of parabolic $\textrm {U}(p,q)$-Higgs bundles, Q. J. Math. 60 (2009), no. 2, 183–233. MR 2506382, DOI 10.1093/qmath/han001
N. L. Gordeev, Products of conjugacy classes in perfect linear groups. Extended covering number, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 321 (2005), no. Vopr. Teor. Predst. Algebr. i Grupp. 12, 67–89, 297–298 (English, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 136 (2006), no. 3, 3867–3879. MR 2138412, DOI 10.1007/s10958-006-0207-6
Shimy Karni, Covering numbers of groups of small order and sporadic groups, Products of conjugacy classes in groups, Lecture Notes in Math., vol. 1112, Springer, Berlin, 1985, pp. 52–196. MR 783069, DOI 10.1007/BFb0072287
Martin W. Liebeck and Aner Shalev, Diameters of finite simple groups: sharp bounds and applications, Ann. of Math. (2) 154 (2001), no. 2, 383–406. MR 1865975, DOI 10.2307/3062101
S. Yu. Orevkov, Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves, J. Knot Theory Ramifications 10 (2001), no. 7, 1005–1023. MR 1867106
S. Yu. Orevkov, Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$, Ann. Fac. Sci. Toulouse Math. (6) 22 (2013), no. 2, 219–251 (English, with English and French summaries). MR 3247775, DOI 10.5802/afst.1371
Julien Paupert, Elliptic triangle groups in $\textrm {PU}(2,1)$, Lagrangian triples and momentum maps, Topology 46 (2007), no. 2, 155–183. MR 2313070, DOI 10.1016/j.top.2007.01.002
Julien Paupert and Pierre Will, Involution and commutator length for complex hyperbolic isometries, Michigan Math. J. 66 (2017), no. 4, 699–744. MR 3720321, DOI 10.1307/mmj/1501812020
Carlos T. Simpson, Products of matrices, Differential geometry, global analysis, and topology (Halifax, NS, 1990) CMS Conf. Proc., vol. 12, Amer. Math. Soc., Providence, RI, 1991, pp. 157–185. MR 1158474

Bibliographic Information

S. Yu. Orevkov
Affiliation: Steklov Mathematical Institute, Russian Academy of Sciences; Institut de Mathématiques de Toulouse, Université Paul Sabatier (Toulouse-3), France
MR Author ID: 202757
Email: orevkov@math.ups-tlse.fr
Published electronically: March 31, 2020
Journal: Trans. Moscow Math. Soc. 2019, 73-81
DOI: https://doi.org/10.1090/mosc/287
MathSciNet review: 4082860