Characters and Automorphism Groups of Compact Riemann Surfaces, Issue 280This book deals with automorphism groups of compact Riemann surfaces, of genus at least two, viewed as factor groups of Fuchsian groups. The author uses modern methods from computational group theory and representation theory, providing classifications of all automorphism groups up to genus 48. The book also classifies the ordinary characters for several groups, arising from the action of automorphisms on the space of holomorphic abelian differentials of a compact Reimann surface. Suitable for graduate students and researchers in group theory, representation theory, complex analysis and computer algebra. |
Contents
III | 1 |
V | 4 |
VI | 7 |
VII | 18 |
VIII | 20 |
IX | 22 |
XI | 25 |
XII | 28 |
XXX | 95 |
XXXI | 105 |
XXXII | 112 |
XXXIII | 119 |
XXXIV | 120 |
XXXV | 126 |
XXXVI | 131 |
XXXVII | 134 |
Other editions - View all
Characters and Automorphism Groups of Compact Riemann Surfaces, Issue 280 Thomas Breuer Limited preview - 2000 |
Common terms and phrases
abelian group algorithm Aut(U Aut(X automorphism group character table characters of G choose class function class structure compact Riemann surface compute condition RH conjugacy classes conjugate consider contains coprime Corollary 12.3 CY(G cyclic group defined denote derived subgroup dihedral group Eichler Trace Formula elements of order elliptic exactly EXAMPLE factor group finite group Fix H fixed points Fixx Fuchsian group G-character genus g group G group of automorphisms group of order Hı(X HECY hence homomorphism hyperbolic Irr(G irreducible character isomorphic Lemma Let G linear m₁ matrix maximal subgroups nonnegative integers nontrivial normal subgroup Note orbit genus perfect group prime Proof Rat(G RH)-character of G RH)-vector Riemann-Hurwitz Formula satisfies the condition Section signature simple groups subgroup H subgroup of G surface kernel epimorphism surface kernel factor surface of genus surjective torsion-free trivial unique values vector ΚΕΙ