Not signed in (Sign In)

Start a new discussion

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 beauty bundle bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched etcs fibration 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 lie-theory limits linear linear-algebra locale localization logic manifolds mathematics measure measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology 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 string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 28th 2021
    • (edited Apr 28th 2021)

    added pointer to Sagan’s textbook and encyclopedia article, and pointer to where in there the Frobenius formula

    s λ=1n!σSym(n)χ (λ)(σ)p σ s_\lambda \;=\; \frac{1}{n!} \underset {\sigma \in Sym(n)} {\sum} \chi^{(\lambda)}(\sigma) \cdot p_\sigma

    is discussed.

    (I did not find it mentioned in either of Macdonald’s, James’s or Diaconis’ textbook)

    diff, v17, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 28th 2021

    Well done! I’d only seen it in Qiaochu Yuan’s post.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2021
    • (edited Apr 29th 2021)

    Yes, thanks, I had followed your links here, where the statement is recorded (out of the blue) as Def. 2 there.

    The only reference given in that post is to

    but I don’t see the formula in there either. In his other post he cites Sagan, though, and so possibly that’s again the source from which he got that formula.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2021
    • (edited Apr 29th 2021)

    I have now made fully explicit (here) all the ingredients that go into the Frobenius formula

    diff, v19, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2021

    added (here) the equivalent description in terms of sums over semistandard Young tableaux.

    (Wrote this as a proposition under “Properties”, but c iting Sagan01, who gives this as the definition. Need to give a reference for the proof of the equivalence to the original Jacobi-style definition.)

    diff, v19, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 16th 2021
    • (edited May 16th 2021)

    made more explicit (here) the formula in terms of ssYT for the case of finite number of variables

    diff, v23, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)