Blob algebra and two-color Soergel calculus
Jorge Espinoza, David Plaza
TL;DR
This paper explores a potential conceptual link between the blob algebra's representation theory and two-color Soergel calculus, proposing a conjecture that connects endomorphism algebras of Bott--Samelson bimodules to blob algebra subalgebras, supported by evidence.
Contribution
It introduces a conjecture relating Bott--Samelson bimodule endomorphisms to blob algebra subalgebras, offering a new perspective on their connection.
Findings
Evidence supports the proposed conjecture.
A new algebraic relationship is suggested.
Potential implications for representation theory.
Abstract
In 2003, Martin and Woodcock noticed a connection between the representation theory of the blob algebra and the Kazhdan--Lusztig polynomials associated with the infinite dihedral group. However, no conceptual explanation for this coincidence has yet been provided. In this study, a possible explanation of this phenomenon is suggested by enunciating a conjecture that relates the endomorphism algebra of Bott--Samelson bimodules to certain subalgebras of the blob algebra obtained by idempotent truncation. Evidence supporting this conjecture is provided.
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