We find the branching laws for the classical pairs GL(m,C) ⊂ GL(n, C),
Sp(2m,C) ⊂ Sp(2n, C), SO(q,C) ⊂ SO(p, C) for all m <= n, and all q <= p, generalizing the well-known results of classical branching laws which exist for m=n-1, and q=p-1. Our approach provides a common proof applicable to all these groups. We also compare the branching multiplicities among these pairs.

This project is part of the author's thesis completed at IIT Bombay. The author expresses gratitude for the PhD fellowship provided by IIT Bombay and IRCC. The author sincerely thanks Prof. Dipendra Prasad, the PhD supervisor, for continuous guidance, support, and insightful discussions--special thanks to Prof. Prasad for dedicating substantial time to reviewing the paper and rectifying errors. The author also thanks Prof. Shripad M. Garge for guidance and fruitful discussions.