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 −...

In mathematics, the special linear group SL(n, R) of degree n over a commutative ring R is the set of n × n matrices with determinant 1, with the group...

converge to a 2-dimensional manifold. The universal cover of SL(2, R) is denoted S L ~ ( 2 , R ) {\displaystyle {\widetilde {\rm {SL}}}(2,\mathbf {R} )} . It...

given by Adg(x) = gxg−1. If G is SL(2, R) (real 2×2 matrices with determinant 1), the Lie algebra of G consists of real 2×2 matrices with trace 0. The representation...

|^{2}-|\beta |^{2}=1\right\},} is a subgroup of Gc = SL(2,C), the group of complex 2 × 2 matrices with determinant 1. If G1 = SL(2,R) then G =...

Mercedes-Benz SL-Class (marketed as Mercedes-AMG SL since 2022) is a grand touring sports car manufactured by Mercedes-Benz since 1954. The designation "SL" derives...

results concerning irreducible unitary representations of the Lie group SL(2, R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra...

the discrete series representations of SL(2,R), the general theory of unitary irreducible representations of SL(2,R) was developed independently by Bargmann...

locally isomorphic to S L 2 ( R ) {\displaystyle \mathrm {SL} _{2}(\mathbb {R} )} or S L 2 ( C ) {\displaystyle \mathrm {SL} _{2}(\mathbb {C} )} and Γ {\displaystyle...

one to exhibit the (2,3,7) triangle group as a specific Fuchsian group in SL(2,R), specifically as a quotient of the modular group. This can be visualized...

time, Harish-Chandra and Gelfand & Naimark derived an explicit formula for SL(2,R) and complex semisimple Lie groups, so in particular the Lorentz groups...

of Sz-Nagy. The result is known to fail for non-amenable groups such as SL(2,R) and the free group on two generators. Dixmier (1950) conjectured that a...

translates under some elements of SL(2, R) contains a punctured neighborhood of the origin. Then all sets in the family A are SL(2, R)-equidecomposable, and likewise...

The R230 generation of the Mercedes-Benz SL-Class was introduced at the 2001 Frankfurt Motor Show and 2001 Bologna Motor Show, replacing the R129. The...

Note that SL(2,R) is a subgroup of this group. The projective special linear group PSL(2,R) = SL(2,R)/{±I}, consisting of the matrices in SL(2,R) modulo...

special function of two variables. It is used in the representation theory of SL(2,R) and in analytic number theory. It is closely related to the Epstein zeta...

2 R {\displaystyle {\mathfrak {sl}}_{2}\mathbb {R} } plays an important role in the study of chaos and fractals, as it generates the Möbius group SL(2...

forms are holomorphic automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its...

numbers appear as homogeneous spaces SL(2,R)/H for the group SL(2,R) and its subgroups H=A, N, K. The group SL(2,R) acts on these homogeneous spaces by...

GL(1, R) Spin(2, 1) = SL(2, R) Spin(3, 1) = SL(2, C) Spin(2, 2) = SL(2, R) × SL(2, R) Spin(4, 1) = Sp(1, 1) Spin(3, 2) = Sp(4, R) Spin(5, 1) = SL(2, H)...

the modular group S L 2 ( Z ) ⊂ S L 2 ( R ) {\displaystyle \mathrm {SL} _{2}(\mathbb {Z} )\subset \mathrm {SL} _{2}(\mathbb {R} )} . The term "modular...

R231 is a chassis code for the sixth generation of the Mercedes-Benz SL-Class roadster, replacing the R230. The car was released in March 2012 and uses...

automorphism group SL(2, R) = Sp(2, R), the Siegel upper half-space has only one metric up to scaling whose isometry group is Sp(2g, R). Writing a generic...

Stationary Low-Power Reactor Number One, also known as SL-1, initially the Argonne Low Power Reactor (ALPR), was a United States Army experimental nuclear...

The Mercedes-Benz R129 SL is a roadster which was produced by Mercedes-Benz from 1988 until 2001. The R129 replaced the R107 in 1989 and was in its turn...

(1,1;\mathbb {C} )} , which is isomorphic to SL ⁡ ( 2 , R ) {\displaystyle \operatorname {SL} (2,\mathbb {R} )} . In physics the special unitary group is...

group SL ( 2 , R ) {\displaystyle {\text{SL}}(2,\mathbb {R} )} acts by unitary operators Ug on the space L 2 ( R ) {\displaystyle L^{2}(\mathbb {R} )} by...

subgroup of SL(2, R {\displaystyle \mathbb {R} } ) is the circle group SO(2), and the homogeneous space SL(2, R {\displaystyle \mathbb {R} } )/SO(2) can be...

SL(2,R) has fundamental group isomorphic to the integers Z, and so SL(2,R) has nontrivial covering spaces. By definition, all finite coverings of SL(2...

covering group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb {C} )} of SO ( 3 ; 1 ) + {\displaystyle {\text{SO}}(3;1)^{+}}...