His playing has a Caribbean influence and bright swinging feeling, with a strong vocabulary of bebop jazz and blues rooted melodies.

[1] He was influenced by Louis Armstrong, Duke Ellington, Erroll Garner, Nat King Cole, Oscar Peterson, Ahmad Jamal, Les McCann, and Frank Sinatra.

Performances at the Carib Theatre in Jamaica by Louis Armstrong and Nat King Cole left a strong impression on the young pianist.

In addition to performing with Frank Sinatra there,[3] Alexander also met and became friends with bassist Ray Brown and vibist Milt Jackson.

In the mid-1970s, he formed a group consisting of John Clayton on bass and Jeff Hamilton on drums, creating a stir on the jazz-scene in Europe.

Jackson used Alexander's trio (with bassist John Clayton and drummer Jeff Hamilton, future big-band co-leaders) for the Pablo recorded LP which was later issued on CD through Original Jazz Classics.

Alexander has also played with several singers, among them Ernestine Anderson and Mary Stallings, as well as with other important leaders (Dizzy Gillespie, Benny Golson, Jimmy Griffin and Frank Morgan).

In his successive trios, Alexander has played frequently with musicians associated with Oscar Peterson: Herb Ellis, Ray Brown, Mads Vinding, Ed Thigpen and Niels-Henning Ørsted Pedersen.