In this paper we first generalize to the case of partial flags a result proved both by Spaltenstein and by Steinberg that relates the relative position of two complete flags and the irreducible components of the flag variety in which they lie, using the Robinson-Schensted-Knuth correspondence. Then we use this result to generalize the mirabolic Robinson-Schensted-Knuth correspondence defined by Travkin, to the case of two partial flags and a line.

Keywords:

partial flag varieties, RSK correspondence partial flag varieties, RSK correspondence

MSC Classifications:

14M15, 05A05 show english descriptions Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Permutations, words, matrices 14M15 - Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
05A05 - Permutations, words, matrices

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