Grassmann embeddings of polar Grassmannians

Ilaria Cardinali; Luca Giuzzi; Antonio Pasini

doi:10.1016/j.jcta.2019.105133

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arXiv · 1810.12811

Grassmann embeddings of polar Grassmannians

Ilaria Cardinali·Luca Giuzzi·Antonio Pasini

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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 [I. Cardinali and A. Pasini, Grassmann and Weyl embeddings of orthogonal Grassmannians. J. Algebr. Combin. 38 (2013), 863-888]) and prove that the Grassmann embedding is a quotient of this generalized "Weyl-like" embedding. We also estimate the dimension of the latter.

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Ilaria Cardinali, Luca Giuzzi, Antonio Pasini. 2018-10-30. Grassmann embeddings of polar Grassmannians. https://doi.org/10.1016/j.jcta.2019.105133

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