You can see some of the shortcuts for Disk Space Analyzer next to the menu commands in application Main Menu.

List of all available shortcuts.

Scan Volume – ⌘-S
Go to root of scanned volume – ⌘-R
Reveal current root element in Finder – ⌘-O
Quick Look current root element – ⌘-Y
Get info for current root element – ⌘-I
Toggle Volume information panel – ⌘-U

List of controls for Sunburst diagram.

Scan Volume – Click on circle center (for not scanned volume)
Switch on/off displaying free space – Click on circle center (for scanned volume)
Open sunburst diagram for parent folder – Click on circle center (for folder circle)
Open sunburst diagram for child folder – Click on folder sector
Show the item in Finder – ⌘-click on folder or file sector
Quick look for the item – ⇧ – click on folder or file sector