Triple

Target class: basis in representation theory
Context triple: [Gelfand–Tsetlin basis, instanceOf, basis in representation theory]

• A. result in representation theory
  A result in representation theory is a proven statement describing how algebraic structures, such as groups or algebras, can be represented by linear transformations on vector spaces and how these representations behave or decompose.
• B. representation of a group
  A representation of a group is a homomorphism from that group into the group of linear transformations of a vector space, allowing the group’s abstract elements to be studied via concrete matrices or operators.
• C. automorphic representation (in a broad sense)
  An automorphic representation (in a broad sense) is an irreducible unitary representation of an adelic or locally compact group that arises in the spectral decomposition of spaces of automorphic forms, encoding number-theoretic and geometric information via harmonic analysis on arithmetic quotients.
• D. projective unitary representation
  A projective unitary representation is a map from a group to unitary operators on a Hilbert space that preserves group multiplication up to a phase factor, i.e., up to multiplication by complex numbers of modulus one.
• E. object in invariant theory
  An object in invariant theory is a mathematical entity, such as a vector space, polynomial ring, or group action, whose structure and symmetries are studied through the functions or quantities that remain unchanged under a specified group of transformations.
• F. None of above. chosen