geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
The representation theory of the general linear groups.
The polynomial irreps of are labeled by Young diagrams (e.g. Fulton 97, Thm. 2 on p. 114).
These are equivalently the irreps of the special linear group (e.g. Sternberg 94, Sec. 5.8).
And for these are also the irreps of the special unitary group (e.g. Peluse 14, p. 2).
hook length formula | hook-content formula |
---|---|
number of standard Young tableaux | number of semistandard Young tableaux |
dimension of irreps of Sym(n) | dimension of irreps of SL(n) |
Shlomo Sternberg, Section 5 and Appendix C.7 of: Group Theory and Physics, Cambridge University Press 1994 (ISBN:9780521558853)
William Fulton, Section 8 of: Young Tableaux, with Applications to Representation Theory and Geometry, Cambridge U. Press, 1997 (doi:10.1017/CBO9780511626241)
Amritanshu Prasad, Representations of General Linear Groups (doi:10.1017/CBO9781139976824.007), Chapter 6 in: Representation theory – A Combinatorial Viewpoint, Cambridge University Press 2014 (doi:10.1017/CBO9781139976824)
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