nLab
combinatorial representation theory

The philosophy of the subfield and explicit approach to representation theory which is sometimes called combinatorial representation theory and the main examples of problems in it is in the influential survey

• Hélène Barcelo, Arun Ram, Combinatorial representation theory, Combinatorics at MSRI in Berkeley: New perspectives in algebraic combinatorics (Berkeley, CA, 1996–97), 23–90, Math. Sci. Res. Inst. Publ. 38, Cambridge Univ. Press 1999.pdf, math.RT/9707221

Related entries include: representation theory, symmetric function, permutation representation, crystal basis, Kazhdan-Lusztig theory, Jack polynomial, Macdonald polynomial, Littlewood-Richardson coefficient?, Schur-Weyl duality?, Schur function, Schur functor, Young diagram

Some other references close in spirit

• P. Littelmann, Paths and root operators in representation theory, Ann. Math. 142, 1995, pp. 499–525.
• Fulton, J. Harris, Representation theory,
• Claudio Procesi, Lie groups, an approach through invariants and representations, Universitext, Springer 2006, gBooks