Séminaire Lotharingien de Combinatoire, 93B.74 (2025), 12 pp.
Yassine El Maazouz and Yelena Mandelshtam
The Positive Orthogonal Grassmannian
Abstract.
The Plücker positive region OGr+(k,2k) of the orthogonal Grassmannian emerged as the positive geometry behind the ABJM scattering amplitudes. In this paper we initiate the study of the positive orthogonal Grassmannian OGr+(k,n) for general values of k,n. We determine the boundary structure of the quadric OGr+(1,n) in P+n-1 and show that it is a positive geometry. We show that OGr+(k,2k+1) is isomorphic to OGr+(k+1,2k+2) and connect its combinatorial structure to matchings on [2k+2]. Finally, we show that in the case n > 2k+1, the \emph{positroid cells} of Gr+(k,n) no longer suffice to induce a CW cell decomposition of OGr+(k,n).
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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