In this paper we compute the dimension of the Grassmann embeddings of the polar Grassmannians associated to a possibly degenerate Hermitian, alternating or quadratic form with possibly non-maximal Witt index. Moreover, in the characteristic 2 case, when the form is quadratic and non-degenerate with bilinearization of minimal Witt index, we define a generalization of the so-called Weyl embedding (see [4]) and prove that the Grassmann embedding is a quotient of this generalized ‘Weyl-like’ embedding. We also estimate the dimension of the latter.

Cardinali, I., Giuzzi, L., Pasini, A. (2020). Grassmann embeddings of polar Grassmannians. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 170 [10.1016/j.jcta.2019.105133].

Grassmann embeddings of polar Grassmannians

Cardinali, I.
;
Pasini, A.
2020-01-01

Abstract

In this paper we compute the dimension of the Grassmann embeddings of the polar Grassmannians associated to a possibly degenerate Hermitian, alternating or quadratic form with possibly non-maximal Witt index. Moreover, in the characteristic 2 case, when the form is quadratic and non-degenerate with bilinearization of minimal Witt index, we define a generalization of the so-called Weyl embedding (see [4]) and prove that the Grassmann embedding is a quotient of this generalized ‘Weyl-like’ embedding. We also estimate the dimension of the latter.
Cardinali, I., Giuzzi, L., Pasini, A. (2020). Grassmann embeddings of polar Grassmannians. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 170 [10.1016/j.jcta.2019.105133].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1124542