Questions tagged [representation-theory]

The systematic study of group representations, which describe abstract groups in terms of linear transformations of vector spaces, such that group elements or their generators are represented as matrices, reducing group-theoretic problems to linear-algebraic ones.

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Isomorphism of Virasoro Algebra with Different Highest Weights

Recently I was reading the big yellow book on "Conformal Field Theory" by P. Francesco et.al, and in appendix 8.A.1, it defined a covariant linear map for fusion process among irreducible ...
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Rotation of spherical harmonics

I have a question about the rotation of spherical harmonics. In Wikipedia it is mentioned that if we make a rotation in 3D space: $R\vec{r}=\vec{r}'$,then the Spherical Harmonics can be written as a ...
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Classifying projective representations

Blagoje Oblak in their thesis "BMS particles in three dimensions” says that "Given a group $G,$ suppose we wish to find all its projective unitary representations. The above considerations [...
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Confusion with Weinberg's QFT book, Volume I, Equation 2.5.3 (one-particle states as irreps of Poincare group)

I am reading Sec. 2.5 of Weinberg's Quantum Theory of Fields, Volume I. There he talks about the classification of relativistic one-particle states according to their transformation under the Poincare ...
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Fermion boundary conditions vs projective representations

I have a basic confusion about the two different boundary conditions for a fermion around a compact direction, periodic versus anti-periodic. We learn in a QM class that a fermion wavefunction picks ...
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For generators of the Lie group under an arbitrary representation: $[T^a,T^b]=if^{abc}T^c$ $[T_A^c]^{ab}=-if^{cab}$ is the generator of the adjoint representation. Is \$\ \ e^{i\theta^d T^d}T^ae^{-i\...