References
- Bai, Z. Q. (2015). Gelfand-Kirillov dimensions of the ℤ2-graded oscillator representations of 𝔰𝔩(n). Acta Math. Sin., English Series 31(6):921–937.
- Bai, Z. Q., Hunziker, M. (2015). On the Gelfand-Kirillov dimension of a unitary highest weight module. Sci. China Math. 58(12):2489–2498.
- Borho, W., Kraft, H. (1976). Über die Gelfand-Kirillov dimension. Math. Ann. 220:1–24.
- Enright, T. J., Howe, R., Wallach, N. R. (1983). A classification of unitary highest weight modules. Progr. Math. 40:97–143.
- Gelfand, I. G., Kirillov, A. A. (1966). Sur les corps liés aux algébres enveloppantes des algébres de Lie. Publ. Math. IHES. 31:5–19.
- Jantzen, J. C. (1983). EinhĂĽllende Algebren halbeinfacher Lie-Algebren. (German) [Enveloping algebras of semisimple Lie algebras]. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], Vol. 3. Berlin: Springer-Verlag.
- Joseph, A. (1978). Gelfand-Kirillov dimension for the annihilators of simple quotients of Verma modules. J. London Math. Soc. 18(2):50–60.
- Knapp, A. W. (2002). Lie Groups Beyond an Introduction, 2nd ed., Progress in Mathematics, Vol. 140. Boston: Birkhäuser Boston.
- Krause, G., Lenagan, T. H. (2000). Growth of Algebras and Gelfand-Kirillov Dimension, Revised edition. Graduate Studies in Mathematics, Vol. 22. Providence, RI: AMS.
- Luo, C., Xu, X. (2013). ℤ2-graded oscillator representations of 𝔰𝔩(n). Commun. Algebra 41:3147–3173.
- Luo, C., Xu, X. (2013). Graded oscillator generalizations of the classical theorem on harmonic polynomials. J. Lie Theory 23:979–1003.
- Luo, C., Xu, X. (2014). ℤ-graded oscillator representations of symplectic Lie algebras. J. Algebra 403:401–425.
- Mathieu, O. (2000). Classification of irreducible weight modules. Ann. Inst. Fourier (Grenoble) 50:537–592.
- Nishiyama, K., Ochiai, H., Taniguchi, K., Yamashita, H., Kato, S. (2001). Nilpotent orbits, associated cycles and Whittaker models for highest weight representations. Astérisque 273:1–163.
- Vogan, D. (1978). Gelfand-Kirillov dimension for Harish-Chandra modules. Invent. Math. 48:75–98.
- Vogan, D. (1981). Singular unitary representations. In Noncommutative Harmonic Analysis and Lie Groups, Lecture Notes in Mathamatics, Vol. 880. Berlin-New York: Springer, pp. 506–535.
- Vogan, D. (1991). Associated varieties and unipotent representations. In Harmonic Analysis on Reductive Groups, Progr. Math. Vol. 101. Boston: Birkhäuser pp. 315–388.
- Wang, W. (1999). Dimension of a minimal nilpotent orbit. Proc. Amer. Math. Soc. 127:935–936.
- Xu, X. (2008). Flag partial differential equations and representations of Lie algebras. Acta. Appl. Math. 102:249–280.
- Zariski, O., Samuel, P. (1975). Commutative Algebra, Vol. II. New York/Berlin(World Publishing Corporation, China): Springer-Verlag.