field of representation theory, a quaternionic representation is a representation on a complex vector space V with an invariant quaternionic structure...

Quaternionic manifold – Concept in geometry Quaternionic matrix – Concept in linear algebra Quaternionic polytope – Concept in geometry Quaternionic projective...

pseudoreal representation. An irreducible pseudoreal representation V is necessarily a quaternionic representation: it admits an invariant quaternionic structure...

mathematics, a quaternionic discrete series representation is a discrete series representation of a semisimple Lie group G associated with a quaternionic structure...

irreducible complex representation of G with Schur indicator −1, called a quaternionic representation. Moreover every irreducible representation on a complex...

v+W\mapsto gv+W} . quaternionic A quaternionic representation of a group G is a complex representation equipped with a G-invariant quaternionic structure. quiver...

A quaternionic matrix is a matrix whose elements are quaternions. The quaternions form a noncommutative ring, and therefore addition and multiplication...

dealing with quaternionic groups it is convenient to represent quaternions using complex 2×2-matrices, With this representation, quaternionic multiplication...

term complex representation is reserved for a representation on a complex vector space that is neither real nor pseudoreal (quaternionic). In other words...

representations of G . {\displaystyle G.} Definition. A quaternionic representation is a (complex) representation V , {\displaystyle V,} which possesses a G {\displaystyle...

argument), one can show that any complex symplectic representation is a quaternionic representation. Quaternionic representations of finite or compact groups...

angle φ. In 3 Euclidean dimensions, the single spinor representation is 2-dimensional and quaternionic. The existence of spinors in 3 dimensions follows from...

that the triple i, j and k:=ij make S into a quaternionic vector space SH. This is called a quaternionic structure. There is an invariant complex antilinear...

In mathematics, quaternionic analysis is the study of functions with quaternions as the domain and/or range. Such functions can be called functions of...

algebraically speaking, the case when ρ is a real representation or quaternionic representation. The Artin root number is, then, either +1 or −1. The...

The Lie algebra of Sp(n) is given by the quaternionic skew-Hermitian matrices, the set of n-by-n quaternionic matrices that satisfy A + A † = 0 {\displaystyle...

representation Semisimple Complex representation Real representation Quaternionic representation Pseudo-real representation Symplectic representation...

U(N) to U(N – 1) states that Example. The unitary symplectic group or quaternionic unitary group, denoted Sp(N) or U(N, H), is the group of all transformations...

Blattner's conjecture Holomorphic discrete series representation Quaternionic discrete series representation Atiyah, Michael; Schmid, Wilfried (1977), "A geometric...

Koca, Mehmet; Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system"...

indicates whether a given irreducible character is real, complex, or quaternionic. They are examples of Schur functors. They are defined as follows. Let...

group is the metaplectic group, which appears in infinite-dimensional representation theory and physics. When one takes for K ⊂ π 1 ( G ) {\displaystyle...

≥ 2. For n ≥ 2, the noncompact Lie group Sp(n, 1) of isometries of a quaternionic hermitian form of signature (n,1) is a simple Lie group of real rank...

Koca, Mehmet; Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system"...

characters of holomorphic discrete series representations. Quaternionic discrete series representation Bargmann, V (1947), "Irreducible unitary representations...

respect to the Riemannian metric g {\displaystyle g} and satisfy the quaternionic relations I 2 = J 2 = K 2 = I J K = − 1 {\displaystyle I^{2}=J^{2}=K^{2}=IJK=-1}...

certain spin representations of SO(3), with respect to the action by quaternionic multiplication. Spherical harmonics can be separated into two set of...

Wolf space to each of the simple complex Lie groups. Quaternionic discrete series representation Besse, Arthur L. (2008), Einstein Manifolds, Classics...

transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform is a...

Koca, Mehmet; Al-Ajmi, Mudhahir; Ozdes Koca, Nazife (2011). "Quaternionic representation of snub 24-cell and its dual polytope derived from E8 root system"...