The bisymplectic Grassmannian \({{\,\mathrm{I_2Gr}\,}}(k,V)\) parametrizes k-dimensional subspaces of a vector space V which are isotropic with respect to two general skew-symmetric forms; it is a Fano projective variety which admits an action of a torus with a finite number of fixed points. In this work, we study its equivariant cohomology with complex coefficients when \(k=2\); the central result of the paper is an equivariant Chevalley formula for the multiplication of the hyperplane class by any Schubert class. Moreover, we study in detail the case of \({{\,\mathrm{I_2Gr}\,}}(2, {\mathbb {C}}^6)\), which is a quasi-homogeneous variety, we analyse its deformations, and we give a presentation of its cohomology.

双辛格拉斯曼式\（{{\，\ mathrm {I_2Gr} \，}}（k，V）\）参数化向量空间V的k维子空间，它们相对于两个一般的斜对称形式是各向同性的；它是Fano射影变种，它允许具有有限个固定点的圆环动作。在这项工作中，当\（k = 2 \）时，我们研究其具有复系数的等变同调。本文的主要结果是等距的Chevalley公式，用于将超平面类乘以任何Schubert类。此外，我们详细研究了\（{{\，\ mathrm {I_2Gr} \，}}（2，{\ mathbb {C}} ^ 6）\）的情况，是准同质变种，我们分析了它的变形，并给出了其同调性的介绍。