Categorifying fractional Euler characteristics, Jones-Wenzl projector and $3j$-symbols

Understand

We study the representation theory of the smallest quantum group and its categorification.

• The first part of the paper contains an easy visualization of the 3j-symbols in terms of weighted signed line arrangements in a fixed triangle and new binomial expressions for the 3j-symbols.
• All these formulas are realized as graded Euler characteristics.
• The 3j-symbols appear as new generalizations of Kazhdan-Lusztig polynomials.