linear group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: SL ( 2 , R ) = { ( a b c d ) : a , b , c , d ∈ R  and  a d − b c...

R). The Casimir element acts on any irreducible representation as multiplication by some complex scalar μ2. Thus in the case of the Lie algebra sl2,...

the expansions of Hauptmoduln. In other words, if Gg is the subgroup of SL2(R) which fixes Tg, then the quotient of the upper half of the complex plane...

construct the metaplectic cover of SL2(R). The elements of the metaplectic group Mp2(R) are the pairs (g, ε), where g ∈ SL 2 ⁡ ( R ) {\displaystyle g\in \operatorname...

Classification of elements of SL2(R) as elliptic, parabolic, and hyperbolic – and similarly for classification of elements of PSL2(R), the real Möbius transformations...

reductive Lie groups this has been solved; see representation theory of SL2(R) and representation theory of the Lorentz group for examples. Warner (1972)...

Table of Lie groups for a list General linear group, special linear group SL2(R) SL2(C) Unitary group, special unitary group SU(2) SU(3) Orthogonal group,...

contractible – see Kuiper's theorem. List of finite simple groups SL2(R) Representation theory of SL2(R) Representations of classical Lie groups Here rings are...

essentially the case where the local field is the real numbers and the group is SL2(R). Whittaker's equation is d 2 w d z 2 + ( − 1 4 + κ z + 1 / 4 − μ 2 z 2...

canonical transformation, a map that preserves the symplectic structure, as SL2(R) can also be interpreted as the symplectic group Sp2, and thus LCTs are...

the new R bayonet series of lenses. Three model of the cameras were sold by Leitz; the Leicaflex Standard, the Leicaflex SL and the Leicaflex SL2. Late...

can be obtained via this procedure; for example, the universal cover of SL2(R), or the quotient of the Heisenberg group by an infinite normal discrete...

mathematics" (PDF). Gazette des mathématiciens (63): 17–36. Langlands, R. P. (1976). "SL2(R), by Serge Lang" (PDF). Bull. Amer. Math. Soc. 82 (5): 688–691. doi:10...

4064/fm-13-1-73-116. Laczkovich, Miklós (1999). "Paradoxical sets under SL2(R)". Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 42: 141–145. Satô, Kenzi...

sitting as lattices inside the (topological) universal covering group SL2(R) → PSL2(R). Further, the modular group has a trivial center, and thus the modular...

becomes clear already in the case of the group SL2(R). The principal series representations of SL2(R) are tempered and account for the spectral decomposition...

\omega )} θ ∈ R / 2 π Z {\displaystyle \theta \in \mathbb {R} /2\pi \mathbb {Z} } (or θ ∈ R / π Z {\displaystyle \theta \in \mathbb {R} /\pi \mathbb {Z}...

fundamental group that has a Thurston geometry modeled on the universal cover of SL2(R). The Rokhlin invariant is a Z / 2 Z {\displaystyle \mathbb {Z} /2\mathbb...

condition is not necessary, as is shown by the case of the modular group in SL2(R), which is a lattice but where the quotient isn't compact (it has cusps)...

transformations Real Möbius transformations (elements of PSL2(R) or its 2-fold cover, SL2(R)) are classified as elliptic, parabolic, or hyperbolic accordingly...

metaplectic groups, which double cover the symplectic groups. The case of SL2(R) involves a fundamental group that is infinite cyclic. Here the central...

communicates aperture setting to the camera. They can be used on later SL / SL2 and R-series cameras in stop-down metering mode only. Leica do not recommend...

to highest weight vectors of certain discrete series representations of SL2(R), while almost holomorphic or quasimodular forms correspond roughly to other...

Tamagawa numbers. The conjecture asserts for the case of the algebraic group SL2(R) that the Tamagawa number of the group is one. That is, the quotient of...

the line bundle is the Möbius bundle, and the spin group is SL2( R {\displaystyle \mathbb {R} } ). In Euclidean signature, the projective plane, conic and...

transformations, which can be visualized as the action of the special linear group SL2(R) on the time–frequency plane, with the preserved symplectic form corresponding...

ISBN 978-0-12-117740-9, MR 0882000 Borel, Armand (1997), Automorphic forms on SL2(R), Cambridge Tracts in Mathematics, vol. 130, Cambridge University Press...

representations are not complementary. For examples see the representation theory of SL2(R). Elias M. Stein (1972) constructed some families of them for higher rank...

He pioneered understanding of the irreducible unitary representations of SL2(R) and the Lorentz group (1947). He further formulated the Bargmann–Wigner...

theory of SO(3) Connection between SO(3) and SU(2) representation theory of SL2(R) Electroweak interaction Rotation group SO(3) § A note on Lie algebras Hall...