In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian...

Arthur–Selberg trace formula is a generalization of the Selberg trace formula from the group SL2 to arbitrary reductive groups over global fields, developed...

the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle a_{11}+a_{22}+\dots...

theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix...

significantly in representation theory, where the character of a representation is the trace of the representation, hence a scalar-valued function on a group χ...

mathematics, the Selberg trace formula, introduced by Selberg (1956), is an expression for the character of the unitary representation of a Lie group G on the...

is the trace. An irreducible representation of G is completely determined by its character. Maschke's theorem holds more generally for fields of positive...

local trace formula (Arthur 1991) is a local analogue of the Arthur–Selberg trace formula that describes the character of the representation of G(F) on...

In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism...

physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the...

analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar-valued function on operators, the partial trace is an operator-valued...

of) the action of G on itself by conjugation. The adjoint representation can be defined for linear algebraic groups over arbitrary fields. Let G be a...

The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations...

Now the character of this representation is defined as the trace of this permutation matrix. An element on the diagonal of a permutation matrix is 1 if...

specifically in representation theory, a semisimple representation (also called a completely reducible representation) is a linear representation of a group or...

The notation Tr V {\displaystyle {\text{Tr}}_{V}} is the trace form on the representation ρ : g → End ( V ) {\displaystyle \rho :{\mathfrak {g}}\rightarrow...

the Church of God of Prophecy—a Holiness Pentecostal denomination. It is best known for the largest representation of the Ten Commandments in the world...

{\text{End}}(V)} be a Lie algebra representation. Let Tr V : End ( V ) → K {\displaystyle {\text{Tr}}_{V}:{\text{End}}(V)\rightarrow K} be the trace functional...

V be a vector space of dimension n over a field F (with n≥2), and let Hom(V,V) denote the linear transformations on V. An n-trace diagram is a graph...

the problem of approximating the Jones polynomial to that of approximating the Markov trace. We wish to construct a complex representation τ {\displaystyle...

finite field arithmetic is arithmetic in a finite field (a field containing a finite number of elements) contrary to arithmetic in a field with an infinite...

concerned with the adjoint representation, and the trace on this representation is the Killing form. For the particular form of the Yang–Mills–Higgs equations...

Field norm Field trace Conjugate element (field theory) Tensor product of fields Types Algebraic number field Global field Local field Finite field Symmetric...

G\to \mathrm {GL} (V)} of a group G on a finite-dimensional vector space V over a field F is the trace of the representation ϕ {\displaystyle \phi }...

of Galois groups in algebraic number theory to automorphic forms and, more generally, the representation theory of algebraic groups over local fields...

theorem applies. See Representation theory of finite groups for a broad overview of the subject of group representations. See Selberg trace formula and the...

to HTTP header field names which are case-insensitive. GET The GET method requests that the target resource transfer a representation of its state. GET...

over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups. The Langlands...

concept of representation theory can be generalized to the case of spherical pair. For example, the relative trace formula is obtained from the trace formula...

copies of -η also fixes the same vector. Hence Co2 has a convenient matrix representation inside the standard representation of Co0. The trace of ζ is -8...