Initial Ideals of Tangent Cones to the Richardson Varieties in the Orthogonal Grassmannian

Table 1

Two subsets of the ring 𝑃=𝔨[𝑋_(𝑟,𝑐)|(𝑟,𝑐)∈𝔒ℜ(𝛽)] and their indexing sets.

Set of elements in 𝑃=𝔨[𝑋(𝑟,𝑐)|(𝑟,𝑐)∈𝔒ℜ(𝛽)]	Indexing set
Monomials of 𝑃/Chains^𝛾𝛼(𝛽)	Pairs of nonempty skew-symmetric lexicographic multisets on 𝛽×𝛽 bounded by 𝑇𝛼,𝑊𝛾
Standard monomials on 𝑌^𝛾𝛼(𝛽)	Nonvanishing skew-symmetric notched bitableaux on 𝛽×𝛽 bounded by 𝑇𝛼,𝑊𝛾