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...

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...

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...

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...

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...

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...

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...

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...

|^{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 =...

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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)^{+}}...

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...

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...

group of the free particle Schrödinger equation. Mathematically, the group SL(2,R) acts on the Heisenberg group by outer automorphisms, and the Schrödinger...

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)...

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...