# Kazhdan-Lusztig representations and Whittaker space of some genuine representations

## TL;DR

This paper establishes a formula connecting the dimension of Whittaker functionals for certain covering group representations to Kazhdan-Lusztig representations, with a refined version verified in key cases.

## Contribution

It introduces a new explicit formula relating Whittaker functional dimensions to Kazhdan-Lusztig representations for genuine principal series of covering groups.

## Key findings

- Derived a formula linking Whittaker dimensions to Kazhdan-Lusztig representations
- Proved the formula for regular unramified genuine principal series
- Verified the refined formula in several important cases

## Abstract

We prove a formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups. The formula explicitly relates such dimension to the Kazhdan-Lusztig representations associated with certain right cells of the Weyl group. We also state a refined version of the formula, which is proved under some natural assumption. The refined formula is also verified unconditionally in several important cases.