Coefficients of the type D Jones-Wenzl projection are expressed as generating functions over Dyck tilings decorated with bi-colored vertical Hermite histories, for both even and odd dot cases.
On the coefficients in the Jones-Wenzl idempotent
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
By studying a categorification of the antisymmetriser quasi-idempotent in the Hecke algebra, we derive a closed formula for the Jones-Wenzl idempotent in the Temperley-Lieb algebra. In particular, we show that when the idempotent is expressed in terms of the monomial basis, the coefficients are the graded ranks of certain indecomposable Soergel modules. Equivalently, the coefficients can be expressed as a ratio of certain Kazhdan-Lusztig polynomials. Similar results are obtained for generalised Jones-Wenzl idempotents in other types.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Jones--Wenzl projections of type $D$ and Dyck tilings
Coefficients of the type D Jones-Wenzl projection are expressed as generating functions over Dyck tilings decorated with bi-colored vertical Hermite histories, for both even and odd dot cases.