Geodesic
Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 621-639.

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We study highest-weight representations of the non-semisimple complex Lie group $D_{n-1/2}$ used for separating multiple points of the spectrum in the reduction $D_n\downarrow D_{n-1}$. In particular, we find formulae for the characters and dimensions of these representations, which turn out to be similar to the well-known Weyl formulae for classical Lie groups.
Keywords: semiclassical intermediate Lie groups, finite-dimensional highest-weight representations, branching rules, weight basis, character and dimension of a representation of a Lie group. 
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V. V. Shtepin; D. L. Konashenkov. Characters and dimensions of highest-weight representations of the intermediate Lie group $D_{n-1/2}$. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 621-639. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a9/

[1] V. V. Shtepin, “Promezhutochnye algebry Li i ikh konechnomernye predstavleniya”, Izv. RAN. Ser. matem., 57:6 (1993), 176–198 ; V. V. Shtepin, “Intermediate Lie algebras and their finite-dimensional representations”, Russian Acad. Sci. Izv. Math., 43:3 (1994), 559–579 | MR | Zbl | DOI

[2] V. V. Shtepin, “Promezhutochnaya ortogonalnaya algebra Li $\mathfrak b_{n-1/2}$ i ee konechnomernye predstavleniya”, Izv. RAN. Ser. matem., 62:3 (1998), 201–223 | DOI | MR | Zbl

[3] V. V. Shtepin, “Promezhutochnaya algebra Li $\mathfrak d_{n-1/2}$, vesovaya skhema i konechnomernye predstavleniya so starshim vesom”, Izv. RAN. Ser. matem., 68:2 (2004), 159–190 | DOI | MR | Zbl

[4] G. Veil, Teoriya grupp i kvantovaya mekhanika, Nauka, M., 1986 ; H. Weyl, Gruppentheorie und Quantenmechanik, S. Hirzel, Leipzig, 1931 | MR | Zbl | MR | Zbl

[5] I. M. Gelfand, M. L. Tsetlin, “Konechnomernye predstavleniya gruppy ortogonalnykh matrits”, Dokl. AN SSSR, 71:6 (1950), 1017–1020 | MR | Zbl

[6] D. P. Zhelobenko, “Klassicheskie gruppy. Spektralnyi analiz konechnomernykh predstavlenii”, UMN, 17:1 (1962), 27–120 | MR | Zbl

[7] A. Barut, R. Ronchka, Teoriya predstavlenii grupp i ee prilozheniya, v. 1, Mir, M., 1980 ; A. O. Barut, R. Raczka, Theory of group representations and applications, Polish Scientific Publ., Warsaw, 1977 | MR | Zbl | MR | Zbl

[8] A. M. Bincer, “Bases in $\mathrm{Sp}(2n)$ representation space”, Group theoretical methods in physics (Cocoyoc, 1980), Lecture Notes in Phys., 135, Springer-Verlag, Berlin–New York, 1980, 459–463 | DOI | MR

[9] V. V. Shtepin, “Razdelenie kratnykh tochek spektra v reduktsii $\mathrm{sp}(2n)\downarrow\mathrm{sp}(2n-2)$”, Funkts. analiz i ego pril., 20:4 (1986), 93–95 | MR | Zbl

[10] G. Veil, “Teoriya predstavlenii nepreryvnykh poluprostykh grupp pri pomoschi lineinykh preobrazovanii”, Izbrannye trudy: Matematika. Teoreticheskaya fizika, Nauka, M., 1984, 100–197 | MR | Zbl

[11] I. M. Gelfand, A. V. Zelevinskii, “Modeli predstavlenii klassicheskikh grupp i ikh skrytye simmetrii”, Funkts. analiz i ego pril., 18:3 (1984), 14–31 | MR | Zbl

[12] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, 3-e izd., Nauka, M., 1985 ; A. I. Borevich, I. R. Shafarevich, Number theory, Academic Press, New York–London, 1966 | MR | Zbl | MR | Zbl