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math.RT2026
Non-canonical Oscillator Representations of Orthogonal Lie Algebras and Pfaffian Varieties
Hengjia Zhang
Associated varieties are fundamental geometric invariants in the study of infinite-dimensional representations of semisimple Lie algebras. Luo and Xu (2013) constructed a large fam…
math.RT2025
Hilbert Polynomials of Noncanonical Orthogonal Oscillator Representations of
Hengjia Zhang, Xiaoping Xu
By applying Fourier transformations to the natural orthogonal oscillator representations of special linear Lie algebras, Luo and the second author (2013) obtained a large family of…
math.RT2025
Orthogonal Oscillator Representations, Laplace Equations and Intersections of Determinantal Varieties
Hengjia Zhang, Xiaoping Xu
Associated varieties are geometric objects appearing in infinite-dimensional representations of semisimple Lie algebras (groups). By applying Fourier transformations to the natural…