Geodesic
Ninth variation of classical group characters of type A-D and Littlewood identities
Mikhail Goltsblat1
1Yale University
The electronic journal of combinatorics, Tome 30 (2023) no. 4
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We introduce certain generalisations of the characters of the classical Lie groups, extending the recently defined factorial characters of Foley and King. In this extension, the factorial powers are replaced with an arbitrary sequence of polynomials, as in Sergeev–Veselov's generalised Schur functions and Okada's generalised Schur P- and Q-functions. We also offer a similar generalisation for the rational Schur functions. We derive Littlewood-type identities for our generalisations. These identities allow us to give new (unflagged) Jacobi–Trudi identities for the Foley–King factorial characters and for rational versions of the factorial Schur functions. We also propose an extension of the original Macdonald's ninth variation of Schur functions to the case of symplectic and orthogonal characters, which helps us prove Nägelsbach–Kostka identities.
DOI : 10.37236/11768
Classification : 05E05, 05E10, 14N15
Mots-clés : Schur functions, Littlewood-type identities, Jacobi-Trudi identities, Foley-King factorial characters

Mikhail Goltsblat  1

1 Yale University 
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     author = {Mikhail Goltsblat},
     title = {Ninth variation of classical group characters of type {A-D} and {Littlewood} identities},
     journal = {The electronic journal of combinatorics},
     year = {2023},
     volume = {30},
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Mikhail Goltsblat. Ninth variation of classical group characters of type A-D and Littlewood identities. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11768

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