Q. How is it that Shavu’ot has no special mitzvot like lulav, shofar, matzot?
A. Some people would disagree with you and argue that cheesecake is a mitzvah. But they are not really right; enjoyable as cheesecake is, there is no obligation to eat it and it is no sin if you don’t.
The deeper answer to your question is that the symbol of Shavu’ot is probably not a noun (lulav, shofar, matzot, etc.) but a verb – learning or living Torah. “Learning” has a special meaning in Judaism. As Ludwig Lewisohn explains it, “It means a devout and seeking attention to the word of prophet or master; it means slaking a thirst of the soul… It desires to understand, not to argue; to find words of life and follow them” (“What is this Jewish Heritage?”, 1954, p.47).
What does living Torah mean? It is not the same as performing rituals: it is to dedicate your whole day, every day, every week, every year to thinking, feeling, acting as a Jew, and it covers the whole gamut of human experience – from how you handle solitariness to how to you handle society, from how you wash your hands to how you treat your customers and employees.