Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: representation theory of the symmetric group

Bottom of Page

1 to 5 of 5

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 28th 2021

    Page created, but author did not leave any comments.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 7th 2021
    • (edited May 7th 2021)

    added this pointer:

    diff, v4, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJan 29th 2025

    added mentioning (here) of the example of the “standard representation”

    diff, v21, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 8th 2025
    • (edited Feb 15th 2025)

    have added (here) statement and verification of the following observation (which may, or may not, better be kept in another entry, such as at parastatistics, not sure):

    The unitarization of the standard representation of the symmetric group Sym3 has two generating transpositions represented by (what in quantum information theory is called)

    1. the Pauli Z-gate Z,

    2. the rotation gate Ry(8π/3)=−Ry(2π/3).

    (After looking through the literature, I feel that this kind of analysis of unitarized symmetric group irreps in terms of standard quantum gates is both relevant and has been missing.)

    diff, v22, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2025

    for what it’s worth, I have streamlined that computation a fair bit now.

    diff, v24, current

1 to 5 of 5

  1.